I have a few doubts on certain phrasal verbs. I hope you can clear them (up)?

1) Can you give me an example of "lay on to"? I can't find any with the preposition "to".
2) He got off with a fine =
He got away with a fine
3) The teacher let them off their homework.
She exempted them from their homework.
4) Get off all that mess from the desk (is there another phrasal verb meaning the same : tidy up?)
5) He is getting on for sixty. He is approaching sixty.
You can't avoid telling him the truth.
You can't get around........ (Do you need a gerund after it?)
6) The bus crashed into the sidewalk and broke down.

I've never heard "lay on to" -- but there's "lay on" and "lay into"

http://www.englishclub.com/ref/Phrasal_Verbs/L/

2. OK

3. The teacher let them off from doing their homework.
(I've never heard this one without the words I've added.)

4. Yes ... "Tidy up that desk!"

5. I've never heard "getting on for" -- This could work, though: "He is getting on in years; he's almost sixty."

Yes, a gerund works, and sometimes a noun or pronoun:
You can't get around it.
You can't get around doing your homework.
You can't get around the boss.

6. Not "into" but "on" -- if you want "into" then change "sidewalk" to "wall" or something vertical!

Sure! I can help clarify your doubts on these phrasal verbs. Let's go through each one:

1) "Lay on to" is not a common phrasal verb. It might be a rare or less frequently used phrasal verb, which can make finding example sentences with the preposition "to" more challenging. In cases like this, it's always helpful to consult multiple sources such as dictionaries, usage guides, or even native speakers to gather more information and examples.

2) You're correct! "He got off with a fine" and "He got away with a fine" generally have the same meaning. Both imply that someone avoided a more severe punishment or consequence.

3) The sentence "The teacher let them off their homework" means the teacher did not require the students to complete their homework. Your alternative sentence, "She exempted them from their homework," conveys a similar meaning. However, "exempted" has a specific connotation of an official or formal exemption, whereas "let them off" is more casual.

4) The phrasal verb "tidy up" can indeed be a suitable alternative to "get off all that mess from the desk." Both phrases convey the idea of cleaning or organizing a messy area.

5) You're correct! The sentence "He is getting on for sixty" means he is approaching the age of sixty. Regarding the second part of the question, "You can't get around" can be followed by a gerund or an object + infinitive form. For example, "You can't get around telling him the truth" or "You can't get around to telling him the truth."

6) The sentence "The bus crashed into the sidewalk and broke down" doesn't contain a phrasal verb but rather two separate verbs. "Crashed into" refers to the collision of the bus with the sidewalk, while "broke down" means the bus stopped functioning properly.