At my old independent chapel, our priest was always in a hurry. He went to a lot of small Mass locations especially on Sunday. Plus his first language was Polish. His sermons were always about 10 minutes long, and he didn't read the Epistle and Gospel.  Instead, the chapel coordinator (an older man, who always wore a suit) would read the epistle and Gospel in English to the congregation while Father silently recited these from the Missale in Latin.

I don't know how "kosher" that is (pardon the term), but that was done for years.

[...] it seemed to me that I read that lay people were sometimes allowed to make some readings in the TLM [....]

A lector ([a.k.a.] reader) in the West is a clerk having the second of the four minor orders. [....]

During the first centuries all the lessons in the liturgy, including the Epistle and Gospel, were read by the lector.  [....]

But gradually the lectorate lost all importance.  The deacon obtained the office of reading the Gospel; in the West the Epistle became the privilege of the subdeacon.  In the Eastern Churches this and other lessons are still supposed to be read by a lector, but everywhere

• his office (as all minor orders) may be supplied by a layman. [....]   Everywhere the order of reader has become merely a stepping-stone to major orders, and a memory of early days.  In the Roman Rite [ in  it] is the second minor order (Ostiarius, Lector, Exorcista, Acolythus). [....]  The lectorate involves no obligation of celibacy or of any other kind. 

I have seen two chapels in which a layman read the epistle and gospel from a lectern in English while the priest read the epistle and gospel at the altar.  Both chapels were independent chapels not affiliated, to my knowledge, with any particular group.

Whether or not this was "legal" or not, I don't know.  I can only attest that I've seen it done.

Here is a photo of St. Pius V Catholic Church in Boston, Massachusetts on
11/22/1964 showing a man reading from a lay lector.  
The Following Sunday was the First Sunday of Advent 11-29-1964 and
the 'Protestant Table' replaced the Altar.
I am an old Schooled Catholic. The Nuns always taught that more grace in
your soul, more you understand the Mass.

In fact, one of the most visible changes in the habitual clothing of nuns after Vat.II was that suddenly everyone could see their hair, whereas before, their heads were covered.  

Little did the public realize that many of the sisters they had seen with hair all covered over actually had no hair at all, because it was all cut off under the habit.  Therefore, by revealing her hair, the longstanding practice of cutting the hair off was abandoned.

Quote from: Disputaciones

Quote from: Neil Obstat

In fact, one of the most visible changes in the habitual clothing of nuns after Vat.II was that suddenly everyone could see their hair, whereas before, their heads were covered.  

Little did the public realize that many of the sisters they had seen with hair all covered over actually had no hair at all, because it was all cut off under the habit.  Therefore, by revealing her hair, the longstanding practice of cutting the hair off was abandoned.

No hair at all? They were bald?

I would think they probably just left it very short for a woman but longer than any man.

Otherwise, how was their hair suddenly visible if it takes a long time for it to grow?

My daughter is a sister in a traditional order.  I once asked her if she cut her hair completely since it's under her habit.  She told me that there are times (seeing a doctor, for example) in which it would be necessary for someone to see her without the habit.  For this reason, though her hair is normally covered, the sisters' hair is still cut to have a "feminine appearance".