LH can't turn a pregnancy test positive. It's possible for an OPK to be positive if you're pregnant, but it isn't possible the other way round, because pregnancy tests only look for hCG which is different. It's possible to have false positives in some cases of PCOS because of a cyst, but other than that it's not really possible with the exceptions of other conditions which can cause you to produce the hormone, but you'd likely know about those.
I have tested this theory out myself during ovulation and wasted some HPTs, all negative. Your strongest LH surge will be when you're about to ovulate, so if it concerns you, and if you aren't pregnant, then try a HPT when you ovulate next and see if it's positive