Currently, there is no way to transfer the ownership of a lookup file from one user to another user. You will have to run the query and save the result under your own account.
In the case of lookup files saved to a shared folder, you will have to use a different file name to save the file since only the user that created the original lookup file has the authority to make changes to it.
Let's say you had a query that was saving the results about new user accounts created each day into a lookup table created by an inactive user. Now, you run the same query with "save" operator to save it in a different table under your own account
Your save operator could look like this:
| parse "name=*," as name
| parse "action=*," as action
| parse "date=*," as date
| where action="sign-up"
| first(date) as date, first(action) as action by name
| save myFolder/mySubFolder/newDailyUsers
The above search would create a file that looks a bit like this: