LAX Controller described a potential ground conflict event. Local Controller cleared an aircraft for take off; prior to crossing traffic being clear of the departure runway.

Narrative

I was observing the operation on the South side of the tower. Aircraft X landed Runway 25L; exited to join Taxiway H Westbound; and was now being taxied across Runway 25R at Taxiway T by the LC1 Controller. Aircraft Y was in position on Runway 25R. When Aircraft X had crossed the majority of Runway 25R; LC1 cleared Aircraft Y for take off. Aircraft X had stopped and not turned onto Taxiway B; Aircraft X still had a good portion of their tail over the Runway 25R hold bars when Aircraft Y was cleared for take off. Aircraft X was just fully clearing Runway 25R when Aircraft Y had rotated; and was passing Taxiway P. I believe that the LC1 Controller knew that Aircraft X was still partially on the runway; but cleared Aircraft Y for take off anyway. Recommendation; I recommend a change in the safety culture at LAX ATCT; because it doesn't appear that they got the memo about the FAA being safety focused. Quite simply; it appears that LAX management is willing to 'play the odds' that if they bend/break the rules; the odds say; nothing will happen.