How do I make sure they will drop me off at Allegiant departure terminal at LAX?
The Guru Take
LAX Terminal 5 - Instruct your driver
Your driver should be aware of where to drop you off as long as you communicate to him or her that you are departing on an Allegiant flight. (With Uber or Lyft, you could drop the pin on an exact terminal, but the driver will most likely as you as you approach the airport.)
Allegiant Airlines' terminal has moved in 2017 to Terminal 5. There's more information here:
Beginning May 13, 2017 Allegiant flights will depart/arrive at Terminal 5.
ippei
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Uber Driver, CEO of TaxiFareFinder and Unleashed, LLC

Comments
LAX really does have challenging logistics, and I myself once got stuck between terminals when the driver dropped me off at the wrong place. That time, I almost missed my flight and literally ran across the parking lot with my suitcase. After that, I became more attentive to routes and services, especially after reading reviews of delta airlines — people there share detailed flight stories and tips for avoiding airport stress. Now I plan ahead and don't leave things to chance.