Presuming LUS flights have moved to T4 bu 2/7, then I would simply go up to the departures level sidewalk and walk clockwise around past TBIT & T3 to T2 - it should take 8 minutes.

It may be quicker to cut across tough the car parks / past the 'space' restaurant building but if unfamiliar with LAX then it may be adventurous.

(You walk up to the Pedestrian crossing just east of T5, go across and into a car park ground floor, turn right iside the carpark and come out at the east end of the building. The old restaurant should be on your right as you continue across to a pedestrian crossing between T2/T3. Then head up to departures)