In a universe where Twi'lek females are often sold into slavery, L'lan makes a point of retaining and expressing her uncommon independence, as well as keeping her precious ship in working order. She willingly works for the New Republic, but insists on her right to refuse a job or to accept work from other outlets, so long as it doesn't conflict with the Republic. When she is teamed with other Republic operatives, she tends to assume control or shout down dissent; L'lan is never the type to meekly obey.
She recently contracted a case of Force ability, which makes her pre-existing slight dislike for Jedi, uh, interesting. (Her partner for several missions has been a rather unconventional Jedi who doesn't seem to mind oogling her or acquiring tinges of the Dark Side, hence her attitude.)
Within her most recent team, L'lan has become known for sleeping nude. She would much prefer to be remembered for piloting her ship and crew away from a Dark Jedi's force lightning than for her sleeping (lack of) attire.