You could schedule it with cron. You usually don't need to update the lists very often though, and you don't want to either as you're just wasting the bandwidth of the hosts of the lists, who aren't making any money off hosting them.
I'm a bit clueless when it comes to that but certainly interested. Could you maybe go into more detail as to which hardware and software is needed to set that up?
So the main software is here https://pi-hole.net/ (and they have good documentation, so I'm not going to repeat the nitty-gritty here)
You obviously need something to run it on, which could be some existing computer that's always on, but (as the name might suggest) a lot of people use some form of Raspberry Pi (or similar) single-board computer.
Pihole will run on basically anything, so you can get an ancient pi and it will still run fine
You can always configure the DNS manually on a device you own to ignore the DHCP settings sent from the router and just go directly to the pihole, obviously not as good as it happening automatically, but a good workaround if that's not possible