We will be in Los Angeles for two days in April. Does anyone have any idea how many lights one can get to in that time?

Well,Point Fermin, Angels Gate and Point Vicente for sure. If you drive south, there would be Old and New Point Loma. There are some very cool lighthouses to the north though. A tour of Point Sur is great, and spring time in Big Sur is beautiful. Schedule of the tour is at Point Sur Schedule First come first serve.
I suggest that you look at the lighthouses and see which ones you have time for and really want to see in addition those close to LA.

Also, to add some more to Laura's reply.

Allow about 2 hours each direction if driving to
the San Diego area, for the Point Loma lights, and about 4-5 hours, depending on your route, going north to the Monterey Peninsula area for Point Sur; and, if you have the time Point Pinos is fairly close to Point Sur.

Have fun, you'll enjoy all of the lights mentioned. Hopefully you have the time to visit them all.

Thanks Laura, Bruce & Judy. We will probably do the LA area lights and also go down to San Diego.