Comments (Meaning / History Only)
Given that Lucas and Luke are derived from a Greek name meaning "from Lucania," I see no reason why the Roman cognomen Lucanus (from which Lucan is derived) cannot mean the same thing.
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After doing adjacent research, it appears that LUCAN < LUCANUS can mean "man from the glade."
LUC- < |lucus| glade, clearing, > grove +
-AN < |-anus| associated man
It is more likely that LUCANIA is a derivative of LUCANUS rather than its root.
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LUC- < |lucus| glade, clearing, > grove +
-AN < |-anus| associated man
It is more likely that LUCANIA is a derivative of LUCANUS rather than its root.
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"... [T]he name Lucca has references that lead to "sacred grove" (Latin: lucus), "to cut" (Latin: lucare) and "luminous space" (leuk, a term used by the first European populations). The origin apparently refers to a wooded area deforested to make room for light or to a clearing located on a river island of Serchio debris, in the middle of wooded areas."
It can be extrapolated that the personal name Lucan means "man from the sacred grove," "man who cuts / clears wood," or "man from the luminous clearing."