Thank you for your question. The Lat Flap has been around for a long time and has a proven track record for breast reconstruction. Although in the category of less elegant flaps, it serves an important role in a plastic surgeon's armamentarium of possible flaps for breast reconstruction.
It is a safe surgery in that your main risks will be risks associated with any medical conditions you have and the typical risks of any surgery (bleeding, infection, scars, etc...) and anesthesia risks. Specifically, the Lat flap has the possible risk of a fluid collection forming on the back from where it was taken. Total flap loss is pretty rare for this surgery unless somehow the blood vessel keeping it alive is not available from previous surgeries.
A typical recovery is off pain medication, driving, and back to a desk job at 2 weeks, sometimes 3. Ask your surgeon what his/her specific instructions are. I defer to your surgeon for all specific instructions, as she/he has had the advantage of evaluating you and doing an examination.
I hope this helps at least somewhat. Best of Luck!