+++Grumbler

WS, to be (very) quick is neither informal, nor colloquial.

TO BE QUICK TO means to no exercise judgement and do things without giving them thought: How can someone who drinks so much be so quick to judge people who smoke?

I think Grumbler’s is the only correct translation here.

Not to exercise judgement and do things without giving them thought means хватать на лету. Right off the bat.

On the fly means to do things in a slipshod manner.

"do things without giving them thought means хватать на лету"

No, it doesn't
хватать на лету означает быстро понимать/усваивать, а не делать

Сделать что-то "на лету" тоже можно, но это уже не "хватать"

It was just a figure of speech.

хватать на лету

• ЛОВИТЬ НА ЛЕТУ что{{}}
[VP; subj: human; pres or past]
=====
1. Also: СХВАТЫВАТЬ < ХВАТАТЬ> НА ЛЕТУ (С ЛЕТУ; ЛОВИТЬ С ЛЕТУ [obj: usu. все, мысль etc; pres or past]
⇒ to (be able to) understand, assimilate sth. (another's thoughts, ideas etc) quickly and easily:
- X ловит все на лету{{}}≈ X picks things up quickly;
- X is quick to grasp things;
- X is quick to catch on (to things);
- X is quick on the uptake;
- [in limited contexts] X catches (seizes) everything on the wing.
Though, On the wing is a mistake here.
`Go and give Mr Scott a hand on the wing, there's a good man.

ON THE FLY means to do something QUICKLY, without any preparation or warning: "When Edgar died, his estranged wife and children created a new will on the fly and forged it, thus inheriting the bulk of his estate." We also use it for people who have a facility for learning or understanding things after only hearing/seeing them one time: He's been studying Russian for three months and already he can understand any question on the fly - he just can't answer right away."

TO BE QUICK TO means to react a certain way without really knowing all the facts: "Don't be too quick to praise my Russian - I understand almost everything I read, but can't speak one word of it."

So which meaning corresponds to НА ЛЕТУ?

скорее, первое
схватывать на лету - быстро понимать
перекусить/поесть на лету (/на ходу)
Только умение регулировать экспозицию на лету может гарантировать хорошие фотографии со свадьбы ...

Don't be too quick to praise my Russian = не спеши...

Thank you, that’s what I thought.

+++Grumbler

thanx 4 your help

Anytime)))

Grumbler, here’s a good example of ON THE FLY I just translated: https://www.lingvolive.com/en-us/community/posts/1192934