The lens reads digital bits. It does not care and does not know how many movies the disc has.
I suspect that the player can't read dual layer DVDs. That's the first function to go.
Here's the usual progress of player breakdown:
First, it can't read dual-layer DVDs. Then it starts getting picky with single-layer DVDs, until it can't read any DVD at all. But it can still read CDs and VCDs. Next, it's the CD and VCD play that get problems.
I don't trust commercial lens cleaners. The best method is to have the unit opened and the lens manually cleaned and adjusted by a technician.