Mage looks like a shortened form of
Margaret (click link), and
Margaret of course means pearl
Lyn is just
Lyn or
Lynn (click link)
The problem with
Lynn is that it has many possible sources
It could be
Welsh:
LakeSpanish: Beautiful
A Germanic Element: Soft, tender
Another Germanic Element: Serpent or Dragon
or just a short form of names ending in
Lynn.
An expert may be able to provide more insight