In 'Alien' she explicitly told Ash that she was in command when Dallas and Kane were off the ship, which is why his decision to disobey her orders and allow them to return to the Nostromo in violation of quarantine protocol pissed her off. I believe she was referred to as the "flight officer," and she remained behind to supervise the repairs to Nostromo after they were damaged in the descent to LV-426.
In 'Aliens,' The Company debriefer van Lewyn (sp?) said:
"...it is the finding of this court of inquiry that Warrant Officer E. Ripley..."
I think the onscreen profiles of each of the crew might have referred to her as flight officer or warrant officer as well. The deal Ripley had with The Company was that her flight status would be reinstated if she went back to LV-426 with Burke and the Colonial Marines.
In Alien3, all of a sudden she was referred to as Lieutenant. This could either be a mistake on the part of the screenwriters or could refer to her reinstated flight status with a promotion for time in service that Weyland-Yutani gave her in Aliens.
Weyland-Yutani's cooperation with (more like exploitation of) the Colonial Marines might require that they give their civilian crews ranks to allow them some control under certain non-combat situations like aboard their ships.
Or their ships operate under a military-like command structure with ranks even though they're civilians, similar to ship crews and airline crews. Or it's quasi-military, like Starfleet.
In the US, Warrant Officers are often technicians and specialists of some type (but can also be pilots), but in the RAF Warrant Officer is a rank between Flight Sergeant and Pilot Officer, so perhaps Ridley Scott was going for that to reflect her pilot status.
[edit] Ninja'd by Candlelight.