I've had an LD reconstruction but it was 9 years ago now, so a lot of the detail's a bit hazy. I only had it on one side. I remember the operation itself was much easier than I expected. It took about 5 hours, but that included the mastectomy, which you've already had. The scars were small and neat, and there was very little pain afterwards. I recovered fairly quickly, had 5 days in hospital and doing normal things at home within a week or so. You'd be very tired for a few weeks though, and will need to do exercises to keep full range of movement in your arm, and definitely no lifting small children for a while! The effect does look good, very natural, and I'm pleased with it overall.
One problem is that I hate the "bulky" feeling in my armpit where they brought the muscle round from the back. I found it incredibly annoying at first, it's like having a rolled-up magazine under there permanently, and I couldn't bring my arm down against my side. They told me the feeling would disappear within a few months, but it's still there, just to a lesser extent, and I'm used to it now.
I haven't noticed any loss of strength in my back, but I do know of people who've refused this operation because they do a lot of skiing or rowing or tennis, so you would need to think about that if you enjoy those things. I find it a bit odd that when I sneeze or cough, my boob jumps because that muscle is round at the front now!
One more thing, I do get eczema on the reconstructed boob, which I think is from the radiotherapy, and of course that skin is now stretched and probably thin. It only started to happen after about 5 years, but it's there more or less permanently now.
Overall, the operation itself is ok, and I'm really glad I've had a reconstruction, but I wasn't given any choice other than the LD approach. If you have the option, then maybe consider some of the alternative abdominal operations before deciding.
Sorry, this is very long and a bit rambling, but hope some of it's helpful 