At present, using out of box functionality, it is not possible to change an existing constituent's lookup ID via a constituent update batch import. The reason for this is that the lookup ID field becomes locked (grayed out) when the constituent is matched to the existing record.
If this is attempted by mapping the constituent system record ID to the constituent field and the desired lookup ID to the lookup ID field, the new lookup ID shows up in the lookup ID field. However, it is not effectively being used or read because, when the imported constituent is matched to the existing record, the lookup ID field is locked. If the batch is committed, the constituent's lookup ID remains the same as it was before.