Doesn't matter whether it's 45 mins or 60 mins. Either way, OP was late. By his own words, he got to LAX at T-60. Let's presume that he was instantly in line. He says that it took 20 minutes to get to the head of the line. That's already 5 minutes late.

DL's rules are clear and consistent with other carriers. LAX is also a physically large airport and 45 minutes is what DL believes it needs to physically get your bag from the counter, through TSA, to the ramp and into the hold in time for an ontime push.

It may have worked before, but that doesn't mean that you can always push your luck. Here is caught up with OP.