In traditional given names (which usually consisted of two words), Mei and Li were popular first parts of the given name. As in Meili, Meiling, Meiwen and other girl's names. Meilan could be written Mei-Lan, Mei-lan or MeiLan as well as Meilan.
In the Disney film Mulan, I think the heroine's name means "brave orchid". So I would say that Lan means just "orchid".
Since Claire means "bright", ClaireLan would mean "bright orchid". :) (Though the Chinese world for "bright" is Ming.)
"You sought a flower and found a fruit. You sought a spring and found a sea. You sought a woman and found a soul. You are disappointed." "It does not become me to make myself smaller than I am." (Edith Södergran 1891-1923)