Would the LacI repressor function as a repressor in eukaryotes if a gene had a single lac operon operator engineered into one of its enhancers?

Yes, simply binding to the enhancer should be sufficient to block transcription by generating a loop of DNA

Yes, as in bacteria, the LacI protein will be able to directly block RNA polymerase from binding to the promoter

Unlikely because the lac repressor needs allolactose to bind to DNA and this would not be present in a eukaryotic nucleus

Unlikely because it functions to repress simply by binding to DNA, whereas most repressors in eukaryotes need dedicated repression domains in addition to a DNA binding domain