Do I get a low tire warning in the heads up display?

No on the low tire warning, but a notice pops up somewhere I'm sure. At least there's an icon that lights up.
As for setting the gear selection display, I'm not sure. I'll be in the car this afternoon, and I'll try to remember to check to see if in fact the gear number does show up and what my setting is to make that happen.

Here's what I see in my car: I get a white D when shifting into Drive, that fades out after about 5 seconds; when shifting gears in the automatic mode, I will get a P, R, or N (in nice colors). The D always fades out and is not "persistent." When moving the shift lever left, over to the manual mode, the HUD shows s1, s2, s3, etc. (I'm not sure what the s stands for). This gear number display is persistent and will remain until you return to Automatic mode.
I can find nothing in my settings that allows me to toggle this on or off. I think it is there by default and cannot be toggled off, like some of the other HUD info stuff.
As an aside, NAV turns are displayed in the HUD only when using the LEXUS nav maps and a destination has been set; they are not displayed when using Google maps or Waze, which is too bad.

The s stands for S mode transmission operating state. The number accompanying the S is the highest gear in the gear range (1 to the S number) the transmission will normally/safely shift to while driving. (The transmission computer will override a driver's S mode selection to prevent damage to the transmission or engine.) For additional details on S mode, see the "Selecting shift ranges in S mode" section starting on page 149 of the 2024 LEXUS ES250, ES350 OWNER'S MANUAL USA AND CANADA ONLY.

You can also get similar behavior with the gear selector in D by using the paddle shifters. Upon pressing the + or - paddle shifter the displayed D will change to Dx where x is the number of the gear that the transmission will use as the highest gear in its normally operating shift range. (Just like S mode there's a computer override to prevent damage.)

Thanks. That info helps a lot.
I knew that the system would not allow over-reving, but it is more complex and sophisticated than I thought.