the Gregorian calendar is the most widespread and currently used calendar among Arab countries.
However, the Kingdom of Saudi Arabia and some Arab countries still retain the authenticity and sanctity of the Hijri date.
I found these 3 answers to the question Do Arabs tell their ages in the lunar calendar?
1. Next solar month, I am going to be 25. I became 25 eight lunar months ago. I choose my age depending on the situation. When I was a teenager I tell people my lunar age although the difference might be several months to make myself look older. On the other hand, my mother uses her solar age, because the difference is more than one year, and you know how one year is sensitive to women.
2. Most Arabs don't use the lunar calendar, it's currently pervasive in one Arab country: Saudi Arabia. They still have the Gregorian "solar calendar".
I know that most people wouldn't tell their ages in the lunar calendar.
The difference is just 10 days per year, it's visible when someone is over 60, but not much of a difference when one is younger (1 year per 35.5 years).
3. Yes. Arabs and Muslims do that. Also when age is used for any religious guide lines or ruling the the lunar ( Hijri ) calender is used. for eg. at 7 we have to encourage children to start praying five times . the puberty age 15 all this are determined using Hijri calender
So it seems there isn't one answer and seems to be a personal choice and changes depending on the situation.