We use kayak.com mostly to research and monitor prices. It may be similar to the hopper app other have mentioned. It doesn't include Southwest, either. They have a phone app, but I haven't tried it, finding the web site easy and powerful.
And then there's LGB, which I haven't flown into or out of. Thought about it for our trip next week but we land just before the rental car facilities close, and the shuttle options were not good, so it was crossed off as well.
I had this concern, but Hertz made it clear in their info that if you give them flight details, they'll stay open for your flight. The clerk was efficient and friendly, and didn't push any upsells.
We were scheduled to arrive around 9:30, landed closer to 9:45. I went straight to Hertz while DH waited for luggage. I was next in line, but the customer at the counter was talkative. Luggage took a while, so I had just finished inspecting our car and heading to the baggage carousel when I ran into DH. By then, it was after 10 (official closing time for the rental agencies), but they were still helping people inside. I'd double check with your rental agency, but I think you'd be fine, and it's a short drive to DLR.
Aside: This was the first time I've ever rented from Hertz, but the
AAA discounted price came in cheaper than Costco, Orbitz, JetBlue, or Amtrak.