No it's not.  Read the quotations I provided from Bellarmine again.  The fact that is being judged is whether or not the Pope is a heretic, not whether he's the Pope.  If the Pope does not "publicly separate himself from the Church," the conviction of heresy is a condition for the ipso facto loss of office to take place.  There's no other way to interpret what Bellarmine wrote without entirely twisting his words.  

If the pope had publicly separated from the Church, then yes, according to Bellarmine the bishops would simply declare that he had lost his office.  But if the fact of his heresy is not indisputably proven by his own act, the conviction of heresy is a condition for the ipso facto loss of office to take place.  Doubtful facts don't suffice.  If his own act does not entirely prove the fact of his heresy, the conviction is necessary to remove the doubt.  Without it, he remains Pope.  

That's why Bellarmine makes a distinction between a Pope who publicly separates from the Church, and one who does not.  In the former case the act of the Pope himself provides indisputable proof of the fact of his heresy; in the latter case the discretionary judgment resulting in a "conviction" (the word Bellarmine uses repeatedly), is what removes the remaining doubt.  

If you read carefully what Pope Celestine wrote, all he said is that the excommunications pronounced by Nestorius and his confreres were null and void, and that those they excommunication remained in communion with Rome. He never said Nestorius was ipso facto deposed before being judged by the Church.

No it's not.  Read the quotations I provided from Bellarmine again.  The fact that is being judged is whether or not the Pope is a heretic, not whether he's the Pope.  If the Pope does not "publicly separate himself from the Church," the conviction of heresy is a condition for the ipso facto loss of office to take place.  There's no other way to interpret what Bellarmine wrote without entirely twisting his words.  

If the pope had publicly separated from the Church, then yes, according to Bellarmine the bishops would simply declare that he had lost his office.  But if the fact of his heresy is not indisputably proven by his own act, the conviction of heresy is a condition for the ipso facto loss of office to take place.  Doubtful facts don't suffice.  If his own act does not entirely prove the fact of his heresy, the conviction is necessary to remove the doubt.  Without it, he remains Pope. 

So does Cardinal Billot, who states that he had lost episcopal jurisdiction from the very time that he began publicly preaching his heresy.

Yes, in our current situation, a heretic pope would retain the material office, but his spiritual office would be impaired...for multiple reasons.  One being that Pius XII's changes to the election laws allow a spiritually impaired pope.  Two being that canon law changes since the 80s clearly allow a heretic to retain office until he is legally deposed.  To partially quote "Croix":  "Sedeprivationism for the win!"
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The issue is that sedevacantists, generally speaking, have drawn a line in the sand and refuse to admit the distinction between the material and spiritual office.  So the debate continues...

Yes, I've spent many months and hundreds of hours studying Bellarmine in both English and Latin.  I've also studied the teaching of all the Church Fathers he references to defend his position on the ipso facto loss of office.

Bellarmine has a lot more to say about how heretical Pope (and heretical bishops) lose their office than most people realize.  Most people have only read his commentary on the Five Opinion, or rather, his commentary on the 4th and 5th Opinions, since that's what the Sedevacantists translated and spread around the internet.  If you only read his commentary on these two opinions, it is nearly impossible to understand what he means, and it is nearly impossible NOT to misunderstand him.

For example, have you ever noticed how Bellarmine appears to directly contradict himself by saying, in the 5th Opinion (and 2nd) that a Pope who falls into occult heresy remains Pope, while in his commentary on the 4th Opinion he seems to say that exact opposite - that a Pope who loses the virtue of faith (i.e., an occult heretic) ceases to be Pope, since "the virtue of faith is a necessary disposition to retain the form of the Pontificate"?   Have you ever noticed that apparent contradiction?  I always noticed it.  I now know that he actually doesn't contradict himself, but you would never in a million years be able to figure out why, if all you had to go on is his commentary on those two opinions.

Something almost no one understands (except John of St. Thomas) is that, in his commentary on the 4th and 5th Opinions, Bellarmine is not arguing that a Pope does not have to be "judged" before being ipso facto deposed.  What he is trying to prove is that a Pope does not have to be authoritatively deposed, to lose his office (since a Pope cannot be authoritatively deposed while he remains Pope).  That's what he's objecting to about Cajetan's opinion, and the contrary is what he's trying to prove in his commentary on the 5th Opinion.  

But again, if you only read the 4th and 5th Opinions, you will easily conclude that Bellarmine believes an antecedent judgment is never required for a Pope to be ipso facto deposed, since he says (in the fifth opinion) that the reason a Pope can be "judged and punished" is because he is no longer the Pope.  But John of St. Thomas says the same and he defended Cajetan's opinion.  Nobody thinks the Pope can be "judged and punished" while he remains Pope, but they all say the Church can "judge" or "legitimately determine" to be a heretic while he remains Pope - all, that is, except those who adhered to the 2nd Opinion, since they had a difference explanation for how a Pope lose his office.

So, I can certainly understand why Dr. Lamont drew the conclusion he did, but it's not what Bellarmine believed.  In fact, it is directly contradicted by both quotations I provided earlier in this thread and by others that I have not yet quoted.