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He is clearly referring to the funeral solemnities not baptism.  

Wrong, wrong, wrong.
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1.  "Mysteries" refers to sacraments.  A funeral is not a sacrament.
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2.  (the most obvious) is your quote is from the book/section titled "Funeral Oration of Valentinian".  St Ambrose was speaking to the grieving catholics at a funeral.  How is St Ambrose saying the funeral solemnities were not done, while speaking at the actual funeral solemnities?
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3.  St Ambrose says, "I hear that you grieve because he did not receive the sacraments of baptism"
He's not referring to a funeral.
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4.  Your quote uses the incorrect singular 'baptism'.  The actual quote says 'sacraments' of baptism, plural.  Why is that?  Because catechumens of the time often received baptism/confirmation together and thus one was NOT considered a full catholic until they had received the (plural) sacraments of initiation.  
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As Pope St Sylvester I said in 325 at the council of Nicea (canon 2):
For a catechumen needs time and further probation after baptism.
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The above is clear proof that in the early church, catechumens could be either baptized or unbaptized.  They were called the same thing.  They were only considered full members of the church until later 1) after baptism and 2) after confirmation (my guess).

Ladislaus, you are truly being disingenuous. You know very well that St. Ambrose’s words DON’T ‘simply say that he received the grace he asked for’. Pray tell me what other grace could he be possibly referring to? To say that it “could be read as the opposite” is plainly bogus.

You MUST tear down this and every other, piece of evidence in order to advance your own home cooked theory, and I’m the one who is of bad will? I’m the one who is not being sincere? Also, what I highlighted in red further confirms that he is referring to BOD. Here are his words again:

No, on the contrary, YOU are reading BoD into this because you want to.  NOTHING in there suggests that this is what he meant, and there's significant evidence that it is NOT what he meant.  I did not "home cook" anything.  I simply looked at the evidence, both ways, and came to the same conclusion as what's below.  I could easily grant it were it shown that St. Ambrose believed in BoD, as that would make him the only Father to hold that opinion and not retract it.

Here's a great treatment of this topic.

https://catholicism.org/baptism-of-desire-its-origin-and-abandonment-in-the-thought-of-saint-augustine.html

The Imperial Catechumen and the Eulogy

Saint Ambrose was the bishop to whom Saint Augustine came for knowledge, under the inspiration of actual grace, while studying in Milan. The holy bishop also regenerated him in Christ. If Saint Ambrose held such a view on baptism of desire, surely Augustine would have cited him as an authority. What is offered by Saint Thomas (and Saint Bernard implicitly) as proof that the Bishop of Milan believed in baptism of desire is his oration in 393 at the funeral of the young Emperor Valentinian II, who was a catechumen, recently converted from Arian influences.

The western Emperor, at the time of his death, was dealing with a rebellion within his ranks led by a pagan general, named Eugenius, and Arbogast, the Count of Vienne. Eugenius wanted to outlaw Christianity in the West and restore Roman paganism. When Valentinian, through the efforts of Theodosius, Catholic Emperor of the East, requested Bishop Ambrose to come to Vienne and baptize him, Eugenius revolted and had the Emperor αssαssιnαtҽd in his quarters. Ambrose was deeply pained and delivered a hopeful eulogy at the funeral in which he compared the deceased catechumen to a “martyr,” slain for the Faith, and “baptized in his own blood.” He said nothing about a baptism of desire, but merely asked the faithful not to grieve over the fact that Valentinian died before he could baptize him. Then, he asked the question: “Did he not obtain the grace which he desired? Did he not obtain what he asked for?” And then he concludes, “Certainly, because he asked for it, he obtained it.” This could easily be an expression of hope that, knowing the danger he was in, the Emperor asked someone to baptize him secretly. Or, it could also mean that the royal catechumen received the grace of salvation because he died a martyr for Christ. Ambrose, apparently, had no proof of the former supposition, for he never mentioned it publicly, but he did have hope that Valentinian’s holy resolve was the cause of his being killed by this murderous usurper who hated the Faith. And that is part of the qualification for martyrdom, along with true repentance for sin. This is what the saint prayed as he ended the eulogy:

“Grant, therefore, to Thy servant the gift of Thy grace which he never rejected, who on the day before his death refused to restore the privileges of the temples although he was pressed by those whom he could well have feared. A crowd of pagans was present, the Senate entreated, but he was not afraid to displease men so long as he pleased Thee alone in Christ. He who had Thy Spirit, how has he not received Thy grace? Or, if the fact disturbs you that the mysteries have not been solemnly celebrated, then you should realize that not even martyrs are crowned if they are catechumens, for they are not crowned if they are not initiated. But if they are washed in their own blood, his piety also and his desire have washed him.” (De Consolatione in obitu Valentiniani, 51-54 = PL 16, 1374-75. Translated by Roy J. Deferrari, Ph.D., in Funeral Orations by St. Gregory nαzιanzen and St. Ambrose, pp. 287-288)

The translation is not the problem here. The last two sentences, which seem contradictory, are exactly accurate from the Latin of Migne’s Patrologia Latina. In the next to the last sentence Saint Ambrose says “that not even martyrs are crowned if they are catechumens, for they are not crowned if they are not initiated.” Does he mean that they are saved, but not crowned? Then, in the last sentence, he says that “if they [martyrs] are washed in their own blood, his piety also and his desire have washed him.” I cannot understand what the holy doctor is affirming or denying in these sentences. Perhaps something is missing from the original transcription itself.

Father Joseph Pfeiffer of the SSPX, in his article “The Three Baptisms” (The Angelus, March 1998), asserts that Saint Augustine heard the eulogy of Valentinian and, consequently, that is why the African doctor believed in baptism of desire.

“One would think, however,” writes Father Pfeiffer, “from reading some of the recent works of the followers of Fr. Feeney that the doctrine of the baptism of desire was held as an obscure opinion amongst some misguided Catholic theologians and saints —saints who got it wrong in deference to Saint Thomas, who believed the doctrine only in deference to Saint Augustine, who held it because he once heard a sermon of Saint Ambrose, “On the Death of Valentinian” . . . Are we to assume that Mr. Hutchinson and like-minded followers of Fr. Feeney have a better understanding of Ambrose than Augustine, his own disciple, who was baptized by the same Ambrose?”

Four quick points: 1) No one supportive of Saint Benedict Center would venture to assume that they would know the mind of Saint Ambrose better than Saint Augustine. That is absurd. 2) As I already noted, if the doctor from Milan intended to identify himself with the speculation concerning baptism of desire, Augustine would have cited his authority, especially if, as Father Pfeiffer assumes, he was “his disciple.” 3) There is no mention of Saint Ambrose’s eulogy for Valentinian in Saint Augustine’s writings, nor are there any known letters of correspondence between them. 4) Saint Augustine began his work against the Pelagians after the death of Saint Ambrose (+397). Again, it would seem likely that in changing his opinion on baptism of desire when confronting the anti-sacramentalism of the Pelagians, he would respectfully at least have made reference to Bishop Ambrose’s alleged contrary view.