Ps2 not reading all of my discs properly

Black PS1 discs and blue PS2 discs are CD-ROMs, silver PS2 discs are single-layer DVDs, and silver-gold PS2 discs are dual-layer DVDs. If your console can read CDs but not DVDs that would indicate that the laser assembly in your drive is either dirty or damaged.

Eject the tray and blow a bunch of canned or compressed air in there to see if it's just a dust issue. If the problem persists you'll need to replace either the whole drive or the laser assembly, depending on how adventurous you are.

PlayStation 2 Optical Disc Drive Laser Assembly Replacement

I cleaned both the lens on the top , and the lens under it. It took tweezers and glasses cleaning wipes and tried it. It was able to read the gold discs. But in the position where I can get the gold disc to read, I cannot get the others that were reading to read.

I'm not entirely sure what you mean by much of that, but if you're saying that you tried cleaning it and you're still having a problem then the solution is to replace the drive or laser assembly.

Sorry, for the non descriptive info. Yes, I took the lid off of the disc drive tray. I cleaned the easiest and most visible lens that is right there in plain sight on the top or outside of the optical drive assembly. Then I took the little black clip off of the optical drive, the clip or plastic piece that fits down over the optical assembly. There is another lens under that floating lens that is on the top. It is a little larger. I cleaned that one with a glass cleaner wipe and put it back together.

Glass cleaner wipe? Like, Windex? Ugh. *Never* use detergents like that on sensitive electronics. Isopropyl alcohol (ideally 99% pure) and a Q-Tip is all you need. Glass cleaners leave behind residues which can corrode metals and fog transparent surfaces (like lenses).