I tested positive for lupus anticoagulant antibodies once and negative for them twice. Apparently they can be transient in the body...you can be negative for it one month and positive the next. My RE recommended low-dose aspirin as well, at 81mg/day, just because of the one positive reading. Low-dose aspirin is generally not associated with any risks to your baby, although the higher dose pills can be dangerous.
After taking low-dose aspirin, I did give birth to a healthy daughter and have another hopefully healthy baby on the way. I am not sure if that is from the aspirin or the progesterone supplements, but I'm convinced one or the other treatment made a difference. I would definitely recommend checking with your doctor on taking it, even if it is for your own peace of mind. It's fairly common for doctors to prescribe heparin also, but mine did not since I only had the one positive reading.
Best wishes and I hope this helps.