It looks like Ink just outputs JSON files, in which case yes, you can. However, it seems like no one has written a Lua runtime yet to interpret those JSON files, so you would have to write your own.
These articles might be helpful if you are interested in doing this:
If you’re not dead set on using Ink, you might take a look at DEFORK - easily create interactive, nonlinear stories, dialogs, conversations, which uses Twine? I’m not sure how the feature set compares.