It appears you arrive (domestically?) and depart internationally on LH the following day. I assume you are spending the night at a hotel or with friends etc.

• If you are checking bags with LH, I believe you have to arrive at the International terminal to do this
• Public transit and almost every hotel shuttle will drop you off at the Domestic terminal only. To get to the international terminal, take one of the shuttle buses near the Marta or shuttle bus drop off point. It's a 10-15min ride to International.
• Once there, you would almost in all cases be better off just entering security there. Even if Precheck is closed, the line usually is short-ish. As mentioned, Pre-check travelers get semi expedited transit, even when PreCheck is closed. Even though I have Precheck, I will often enter at the International terminal because the regular line can be shorter than domestic Precheck at certain times. If nothing else, you can look at the line and decide, but presume going back to Domestic will add 15-25 min to your time to get through
• If you enter at International, your departure gate will be right there at Concourse F (past security) or Concourse E, which is one stop on the underground train.

If you have no bags to check, you could theoretically check in with LH online and use your BP to enter security (via Clear/Precheck) domestically and take the underground train to E/F to depart.

If anyone knows of a airport hotel that will drop you off at International departures, that would be a good nugget of info. You can maybe tip the driver to do this, but would assume YMMV.