Of course, in actuality her two personalities are two facets of the same personality, and eventually Ran mends her relationship with Lum little by little, as Rei and Ran start to spend a little time with each other (Lum no longer has any interest in the empty-headed Rei, although he still seems to want a relationship with her) .
For sure, Ran always had it hard, as the weakest of all her alien friends (Lum can fly and shoot lightning bolts, Benten is extremely tough and a powerful fighter, and Oyuki can control cold and ice at will) - Ran's only power is the ability to cause another to age by kissing them (and willing it). Although an alien herself, her only alien feature is pointed ears (which she often hides behind her hair when in her Earthling guise of Ran (蘭)). Although she sometimes tries to make up for her lack of strength by using alien machinery or artillery, her much stronger friends easily overpower her (after which she quickly apologizes, or flees!).
In the end, though, Ran is one of my favorite characters for some reason!