I don't understand - I am new to this. Are you posing a question?
If so, here goes my attempt at answering.
Phelip:I haven´t see you lately!Where have you been?
Lia:Oh,I´ve made a break.I´ve decided to take english lessons and stop playing tennis.
I believe that the expression "I've made a break" in this case does not refer to "dar um tempo" but rather it makes reference to make a "clean break or stop something, brake ties" - in this case, start something new. Stop the tennis and start the English lessons.
Make a break - also can imply to make a run for it, an attempt to escape, run from the past, etc...the use of it in this sentence would be correct albeit somewhat odd.
If the intent was for Lia to say that she has taken a break from on to start another then she should have said: Oh, I've taken
a break (from tennis)
. I've decided.....
Ok, sorry, I think I may have overcomplicated my response. Hope this helps rather than confuse.