I have a string of lights with a chinese 2 prong plug. An adaptor seems to cost a lot more than the lights. Can I just cut the plug off an old lamp and replace it?

In China they use 240VAC. In the US, 120VAC. If you put on 120VAC, you can use but it won't be very bright. Just use a 2 prong indoor plug. You can also change the bulbs to 120VAC but it's probably cheaper to just buy a string of Christmas lights and use them.