Cranks but Doesn't Start
 

I have a 2018 RX 350 with about 90K miles on it. The other day, I drove the car for about 45 minutes, and parked it for about 4 hours. When I came out to start it, I pushed the Start button and the engine cranked for about 5 seconds, did not start, and then "start sequence" stopped. So I tried it again. (I may have held down the Start button this second time instead of pushing it and then releasing it.) It took several seconds but the engine eventually started. It was a little rough at first but it smoothed out and ran normally after that. There was no Check Engine light and later, when I checked for codes, there were none. The car/engine seemed to start and run normally for the few time I drove it since.

Two days later, I drove the car a few times and parked it in the garage. About 9 or 10 hours later, I went into the garage and heard a strange hum coming from near the underside-rear of the car (although, not sure of the exact location). I thought it might be the fuel pump, but was not sure. I got into the car (while it was still "humming") and tried to start it. The car exhibited the same behavior as I described, above, but it did eventually start. The car sat overnight in the garage and I just started it and it started normally. And I just checked for codes again and there are none. (These intermittent problems are maddening.)

I have done a little research and found some suggestions saying the noise might have been from the EVAP system (EVAP leak detection).

Does anyone have any ideas about what this might be, what I might try next, or how to diagnose the problem?

I would certainly have the battery load-tested at one of your local auto supply places.

Battery? Hmm. I'll have to think about that. The car is not showing any signs of a battery problem. I mean, it sounds like the starter would turn the engine forever if I needed it to. What is it that makes you think it could be the battery?

It costs nothing and it's one thing to cross off the list.....or not.

With no codes, will be harder to pinpoint…. Couple of things to look at/try:

When cranking but no start, keep eye on rpm gauge, does it move ever so slightly? If it does move, can rule out crankshaft and camshaft position sensors.

In a crank, no start, could spray brake cleaner into throttle body (after MAF), if car starts right away, points to a fuel delivery issue.

Also, good to keep an eye on the battery, crank no start can spank a battery fairly quickly.

Remember FAST: fuel, air, spark and timing. Basic components needed…

It has been a few months, since my original post. The problem that I originally described is still happening but very infrequently. That problem being, I push the Start button, and the engine cranks for several seconds and does not start and the engine-start process quits. When I push the Start button a second time, the engine eventually starts, but it runs rough for one or two seconds then smooths out.
I had the battery checked at an Auto Zone and was told that the battery was good.
I connected an ODBLink MX+ scanner and used it to read the Fuel Rail A Pressure and the Fuel Rail B Pressure. When the engine is running, The Fuel Rail A Pressure is up around 1000 to 1200 PSI. The Fuel Rail B Pressure is around 50 to 60 PSI. I think these numbers might be normal. Someone on this forum might verify that for me.
After the engine sits for a few hours, the Fuel Rail A Pressure drops to about 40 PSI. The Fuel Rail B Pressure maintains its 50 to 60 PSI. (Although, when I put the car in Accessory mode, I can hear the in-tank fuel pump running and that might be pressurizing the B Rail and that is what my scanner is reading.) I am guessing that the Fuel Rail A Pressure being so low is not normal.
The problem with diagnosing this problems is that, even after sitting overnight with the A Rail pressure so low, the car will most often start normally. As the engine cranks and starts, the Rail A pressure jumps quickly from 40 to 200 to 900 to over 1000 PSI and the car appears to start and run normally. Other times, though not very often, the engine will not start or it will start rough.
So, are there any suggestions on what I might look at or look for next?

Before starting the car, switch the ignition on and wait 5–10 seconds (don’t press the brake; press the start button twice), then start it. If the car fires up right away, you’re likely dealing with a fuel issue—most likely in the high-pressure system. Test this multiple times to verify the pattern.

Thanks @Lex2000TL . I have a question that maybe you (or someone else) can answer. In your latest reply, you said, "If the car fires up right away, you’re likely dealing with a fuel issue—most likely in the high-pressure system." Is the thought or expectation here that if I turn the ignition on and wait 5 to 10 seconds, this will allow for the high-pressure fuel rail to pressurize? If that is the case, then I should be able to connect my OBDLink scanner and see the pressure in the high-pressure fuel rail rise before I crank the engine. Is there something else I should be looking at or looking for?

More Info: I followed the instructions from @Lex2000TL , but this time I connected my OBDLink scanner. I turned on the ignition (without starting the engine) and collected the high-pressure fuel rail (Fuel Rail A) data for about 60 seconds. The Fuel Rail A pressure was steady at about 47 PSI. Then I started the engine. It started normally and within 1 second, the Fuel Rail A pressure was up around 1,800 PSI.
Does that information provide any hints at a potential problem?

There appears to be a leak in the fuel system (possibly internal), resulting in a gradual loss of pressure. When starting the vehicle, the fuel pump must rebuild pressure during cranking. Before adequate pressure is reached, the system stops the cranking process.
Pressing the start button twice primes the system by activating the ignition and low-pressure fuel pump without engaging the engine, allowing pressure to build in advance. This explains why the vehicle starts normally afterward.