Zij ziet eruit als haar moeder.

What is “eruit?” could you use “lijkt”?

Literally “eruit” would mean “out of it”, which can also be split up into “er … uit”
“Er kwam een raar geluid uit” - “A strange sound came out of it”
“Ze gooide hem eruit” - “She threw him out (of it/the place)”

However, in this case it’s used as een expression “eruit zien als” - “to look like”/“to resemble”.

You could indeed substitute it with “lijken op” (be sure to include the “op”) as follows:
“Zij lijkt op haar moeder”

To be honest, I would normally only use the “lijkt op” version.

I would only use the “eruit zien als” version to say something along the lines of “Zij ziet eruit alsof ze een week niet geslapen heeft” - “She looks as if she hasn’t slept for a week”, “Hij ziet eruit alsof hij moet hoesten” - “He looks like he has to cough”.