I would ditch the lookup field (if you mean a field in a table). Perhaps tblDepts and tblCompanies and a junction tblCompDepts to relate the two, assuming that this isn't about just one company. Same for tblSponsors and junction to relate sponsors and companies. That setup ought to solve your problem except (for me) numbering sponsors as both 3 and 4 doesn't help to clarify things.
Or is it sponsors relate to departments?? Then your junction tblSponsorDept could group companies with departments but if you don't include the sponsor ID in this table, you need another table. That would probably be simpler but strictly speaking, not completely normalized. If you are rusty, then perhaps you should review database normalization and try applying it to your process. Then plan this out on paper before creating any db objects. Post back if you want feedback on the schema you arrive at. Last but not least, if you don't completely understand the nature of table lookup fields, I cannot help but wonder what your naming convention is, or what is the chance that you'd use table level calculated fields (another no-no).
The more we hear silence, the more we begin to think about our value in this universe.
Paraphrase of Professor Brian Cox.