Well honestly speaking,I didn't have any great strategy for RC . I have been quite a voracious reader and read stuff right from Bronte to Salman Rushdie and have interests in areas ranging from all genres of music to human psychology ,and from open source technology to economics,history and what not! Haha. Why I am listing all these things is to show that RC is all about your comprehension ability.You have to be read fast and at the same time comprehend properly.
Well coming back to the RC strategy,there are only two tips which I found to be of great use
1.Read the first line of each paragraph carefully . The first line ,in most of the cases, is the key to the door.
2. Take small breaks of 5-6 seconds after reading a paragraph otherwise the more you force yourself to comprehend the lower you'll actually comprehend.
Both the above strategies really worked for me.
I'm not sure how the passages in the LSAT RC document are but you may want to use
RC99 . Since the passages and the questions there of the standard GMAT pattern ,you may want to time yourself on those passages.