Is there a link between dry eyes and dry lips?

Possible: There is something called sjogren's syndrome that includes dry eyes and dry mouth. They can be linked.

Dehydration?: Though it might seem too obvious, not drinking enough water to replace what you are losing with sweat, urination, etc. Should be the first thing to consider - water, not soda, coffee, juice or other sweet drinks. If this does not solve your dryness, you might need to see your physician for a possible health reason for it.