Xbox 360 that doesn't read games well

I was giving a 360 so I had a gift for my daughter she wanted. Now I have an issue, it'll play DVDs but will give me an error message of unable to read after game start up screen. This is only one out of 6 games I tried.

So my question is do I buy a lens cleaner or skip that and buy a new DVD drive for it? I just want it fixed before Christmas.

I was told to take it apart to see what had been messed with but I don't plan on sending it.

If the DVD drive works for some games, try reading the not-working game's DVD on your computer, because the problem will most probably be on it - it's likely damaged physically (maybe the damage will be visible), or maybe the content is corrupted.

If the drive works with no game, the problem is on it (or on all the games). You should, as you said, investigate the lens (and other components), or change the whole drive, what fits you more. It's not very important which you choose (usually the main criterium is the cost).

You could also just go to the nearest shop with XBoxes and discuss the problem with the staff.