Are they the very small lights?

While some have a built in connection (in each bulb) to keep the entire string from going out when a single bulb fails, they do not work well when multiple bulbs in the strong have failed.

A battery powered bulb checker and some time going through every bulb might be worth the trouble.

Yeah, use a bulb checker for your type of lights. If your lights (as most pre-lit trees) are incandescent mini-lights, you may have had a few fail.

As for replacing the tree, I would only do this if the tree itself no longer fits your needs. Frankly, before doing this, I would consider removing the pre-lit strings and just trimming the tree with replacement strings of longer-lasting LED lights.