"Having been a gymnast," = her experience of this. She had stopped being a gymnast in the past. "Being a gymnast" = she was a gymnast at the time.

I reckon,you should should use the second sentence,when referring to 'present situation',i.e,Being a gymnast,i am well aware of the importance of exercising daily.The first sentence is generally used,while talking about the past and your 1st sentence certainly sounds quite good to me.You can also say:Having been a gymnast 2 years ago,Lynn knew the importance of exercise.:D