This is probably the position that is the most different routine from store to store, based on the schedule.
First, I would check in with your store director, if available. Always ask about attendance. Whoever the "mid LOD" is check in with them, and ask them about attendance as well. Any other leader in the building check in with them, even if only briefly, before walking the floor.
If you have an RDC truck that day, I would then head to receiving, and make a list of any and all remaining push. Write down each type of vehicle, and the type of product on it. This is very important for holding team members accountable.
Always check reshop at guest service and the fitting room within your first hour. If its a mess, get in touch with your leadership team before hand off. I have had my style lead come back at me the following day saying "we rolled too much reshop" when in reality she was there when it all accumulated.
One note on the lead check ins: you are the only person working mon-fri, everyone else gets 1 weekday off. If tuesday is when your style lead is gone, check in more closely with your style consultants. If Wednesday is the day when your consumables lead is gone, check in with your consumables experts.
Most important note: the closing lead does not come up with the plan for executing the day's tasks, but you do have to execute that plan. My first month was chaotic because I let my peers get away with not having a plan - or making an impossible plan then blaming me for things not going their way. Challenge your pers on their plan when they're wrong. I had a style lead tell me my 4 hour closer should be able to deep zone all of style and leave no reshop in 4 hours. This was clearly insane - but because I did not go to my SD with her insane plan immediately, she could get away with saying I accepted her plan.
Utilize your team, and audit your schedules: it is incredibly easy for other leaders to say "I dont need a closer, i dont work past 2, 4, or 6, its not my problem" if there is a scheduling gap at night, I take the lead on getting it covered - theres no reason for HR or the lead for that area to care if theyre not working at that time. Also, know that you can do what you need to do with your team. When I had two cashiers call off the Friday before mothers day, while I didnt like it, I pulled everyone on the floor up to the lanes for at least an hour. Did push roll? You bet, but we made sales - and believe me, nobody is picking up a friday closing shift for fun.
Don't get stressed. You are there to 1. Observe 2. Report 3. Secure 4. Teach 5. Train 6. Help guests. I spend about 50% of my time observing behaviors and correcting them. There is nobody else there at night, maybe one other lead until 7ish, if you do not correct bad behaviors, it wont happen. I spend probably 5% of my time with individual guests, another 5% securing the building, 5% communicating with other leaders via email, 10% in person, and 25% of my time evaluating/walking the zone (always with a 3tier for reshop). However, that balance can get blown up when I spend 50% of my own time at guest service because hours are tight and we're beating sales.
Early on, status with your SD alot, get a sense of his or her priorities. Once you get a feel of what they feel is important, your general rhythm will go lime this: focus on push on RDC truck days, focus on the zone on non truck days. If you have a truck everyday you work, I would focus on push for the first half of your shift, and the zone in the second half of your shift.
Lastly, every store, and every different day, will have its specific quirks. On Tuesdays I head straight back to SFS because their ETL is gone that day, and their TL leaves 30 minutes before I get in. I also check the 3pm cafs to make sure their assignments are being followed. On fridays I walk milk because it gets delivered right before I punch in. On monday I status briefly with HR to make sure we're on the same page for any potential corrective action or upcoming terms.
Phone numbers: get all the phone numbers you need to be an LOD into your phone. Alert one, fmoc, csc, stanley, your apbp, your pmbp. Also, you will likely never see your PML, I see mine only in passing - get their phone number just in case, PMs can know things about a building that nobody else will.
Lastly, as with every job with this company, dont take it personally - especially when you do not have a specific department reporting to you. Literally every other leader in the building is responsible for fixing their department. While you can help, you shouldn't and heres why: they will never appreciate it. My first month I thought I was helping so much by setting endcaps at night, then I realized I was just a crutch for a dysfunctional GM team. What happened when I stopped setting? They actually had to teach their team how to set. Think of yourself like a thinly spread security blanket for the whole store, you can stop bad situations from getting worse, and guide people in the right direction, but they have to make their own choices. You making those choices for them fixes nothing. Maybe for one night, but it ignores the underlying problems entirely. You are there for stability and security, and following up. You can help diagnose problems, but each department owner must fix it themselves - otherwise they wont grow as leaders as well.