El Capitan (or newer OS) on a MBA late 2010 I've an "old" MacbookAir 11" (late 2010, 4GB of RAM, 180GB SSD), which I've loaned to a friend.
Now he gave it back to me, and I'm planning to use it as a "mobility" machine.
My problem is that the applications I use (Mathematica 11, Office 2016, etc) require at least El Capitan.

What I want to ask is if someone is in a similar condition - same generation of MBAs, same (or newer) OS - and what are his feelings. Is the system fast enough? Does it have annoying lags?

PS: my "typical" working session is made by Chrome (~40 opened tabs) + Acrobat or Word (2 files open) + OneNote.
Late 10 Macbook Airs can run Sierra - so your difficulty may be in obtaining El Capitan if that's what you would prefer, which you can only get if it's already in your Purchase History on the App Store.  

Everything else in your question is really too opinion-based to garner useful answers.

Ref - EveryMac