My answer to that would be yes. I had a ps2 that would read ps1 discs and audio cd's but refused to read ps2 dvd games or dvd films. Sometimes re-aligning the lens screw sorts it but it's still risky if you're not sure what to do.
Are you getting any rattly noises from you're drive or clicking?
sounds like maybe the laser arm guide is worn/loose or you can try adjusting the small screw next to the laser (opposite side of laser arm guide). don't adjust too much though or you will scratch the disc. I'm quite new to the ps2 scene myself so if i'm wrong then someone correct me quick, i don't wanna be gettin the blame for screwin up someone's console.
Hard to explain, you have the two guide bars, on the right when you look at the front of the drive, you have the laser arm guide that runs through the worm motor and on the left you have a small metal part showing with a really small screw (usually black) that adjusts the angle of the laser. that small screw is the one i mean.
However, that is only for a click or two. if you're getting a lot of clicking/buzzing its prob the laser arm on the right that needs adjusted or replaced. it looks like a small thin strip of metal with a white bit of plastic in this sorta shape.
_____
|=======|_____|
___| || ||
normally taking it of off and bending it down a bit (not too much) will sort the big buzz/click sound out.
Edit. that ascii pic didn't work here's what i mean
Well, i would try the small black screw on the other guide then, just a little bit at a time though, you don't want to scratch those discs. is it original or back-up discs you're using? if original, then i would say the laser is packing in more than anything else but if back-ups then try just a small turn either way (clockwise i think) if that don't fix it then it's time for a new laser (or ps2).
Sorry, can't be much more help than that. like i said, i'm fairly new to the ps2 scene, much more used to the XboX.