LH does not have a peak surge (as in as high as ovulation) just before af, but it can rise to give a near positive opk, some women say they get a true opk too.
This endotext website gives great detail on the smaller rises that can occur in LH during the lueal phase Quote: "The secretion of progesterone and estradiol during the luteal phase is episodic, and correlates closely with pulses of LH secretion (Fig. 8) [50]. The frequency and amplitude of LH secretion during the follicular phase regulates subsequent luteal phase function and is consistent with the regulatory role of LH during the luteal phase [51].
If you look at the graphs on this website you can see the slightly higher peak that shows up just at the end of the cycle. This is what I have in the past picked up with an extremely near positive opk test, just before af arrives, also leads to the change in cervical mucus just before af arrives too.
There are plenty of other websites where women ask why this happens, it is a fairly common occurance,
The other side of it is, that Multiple positive opk's can occur with annovulatory cycles too.
"Luteinizing Hormone (LH), which is detected by Ovulation Prediction Kits, may be elevated even when you are not immediately approaching ovulation. This can cause you to see multiple positive OPKs. When this happens, you will probably ovulate just after the last positive OPK if you continue to use the kit, though this may occur in anovulatory cycles as well. Nonetheless, you should treat any positive OPK reading as meaning that you may be about to ovulate." www.fertilityfriend.com/courses/lesson.php?p=1;15;0;0
I hope this answers the questions as to how you can get an apparent positive opk before your period.