I have the following sentence:
I've got a lot of things to get done by this weekend.
Is it correct? Is to get done a valid causative form?
In the original example
get is used twice, in two different idioms
with quite different meanings and grammar. Get is like that; it's a busy verb.
You don't seem to be concerned with (1), but plenty of folks puzzle over why people say things like I've got a cold instead of I have a cold, or You've got to see it instead of You have to see it.
(2) is a relative infinitive construction modifying a lot of things, but that's not an issue, either. Rather, it seems to be the causative get
NP done infinitive idiom that is somehow troublesome.
This is just the get version of the causative have construction
or the causative be construction
Since get is the causative/inchoative of both be and have,
is an obvious choice.