Avoid Centralville and The Acre, they're fine for passing through in the day and a lot of the crime is drug or gang related. But you probably don't want to live there, and you can avoid them at night to be safe.

Appleton St downtown has some shady characters.

Upper Highlands and Belvidere are the nicest neighborhoods of Lowell.

Also I forgot to add, I kinda just assumed you were a man because of the dumb internet stereotype. But if you're a woman that may change whether you want to live in Lowell or not. The city has cleaned up a bit but it's nowhere near as safe as the surrounding suburban towns. I know many women in the area would not feel safe wandering around Lowell after dark by themselves. But it's really dependent on you, statistically the crime is around the US average, but some people worry about crime more than others.