Is there a single adverb meaning 'in common'?
The adverb commonly in the sense of 'in common' is now obsolete as shown in this wikitionary:
as a rule; frequently; usually
(obsolete) in common; familiarly
Is there a single adverb ending with '-ly' that can be used instead of 'in common'?
Here's an example:
Intersecting lines have one point in common.
If two things have X in common, you can say the two things share X. You could also use the adverb jointly.