Hey Cap'n,
The L7 is most definitively an e23. The L designation was for luxery and besides the L7 badge on the trunk, the easiest way to identify an L7 from a 735i is the miles and miles of leather. The headliner, dash, glove box, center console, under steering wheel cover and door panels that were not normally leather covered on the garden variety 735i are covered in the L7. And that is basically the ONLY difference between a 735i and L7.
For the best e23 resources, go to:
http://www.bimmerboard.com/forums/e23
http://bimmer.roadfly.com/bmw/forums/e23
Join the boards and don't be afraid to ask questions. The archives on both sites are extensive and I bet that whatever problem you are having has been discussed at one time or another. Just putting the search term "L7" in either site will give you more information than you expected.
Solutions abound! Enjoy your fancy e23!