Alkaline batteries in parallel with lithium cell?

Any difference in voltage between the batteries will cause current to flow from the higher-voltage battery to the lower-voltage one.

If this makes you feel uncomfortable, it should. It's not a good idea to run batteries in parallel, unless there is some mechanism (such as a series diode) to block this flow.

Lithium coin cells aren't horribly expensive, especially if you buy from a mail-order supplier. You can use the opportunity to stock up on batteries you need for other stuff you own.

Short answer is NO! Since you give ZERO clues as to what size batteries, or what voltages your unspecificied system can tolerate, or what you consider a problem, you can't expect even an approximate answer. But a careful person would still say, NO! Take out the lithium cell.

Or isolate it with a diode.