When your laptop is sleeping, it can't be doing computation. I mean, that's not specific to LLMs. You're going to have to set it in your OS to not sleep if you want to remotely access it, or to sleep under conditions that don't arise for you (e.g. "don't sleep if the lid is closed while the laptop is plugged in" or whatever).

The only exception I can think of would be if you (a) have it connected to wired Ethernet and (b) the laptop can do Wake-on-LAN; in that scenario, you could rig something up where it wakes up when something tries to contact it. In practice, you probably just don't want to have it sleeping.

Disable sleep/hibernate on your laptop. Disable sleep/hibernate/poweroff when lid is closed. If you're going to treat your laptop as a server, probably better to configure it as a server.

I use my homeserver for it. It's located in the broom closet and on 24/7. But there's ways to do it with a laptop. You can inhibit standby and let it run contunuously. Or configure Wake on Lan and wake it up before you use it... I mean a switched-off computer obviously can't do any computation.

You can run Ollama locally on a phone through Newsboat, though beware it can be very heavy on the device.

Use https://anythingllm.com/ on your mobile with its own local models? You'll be limited with your phone's hardware but it will do on a pinch where you can't reach or use your laptop. It's open source and everything works locally.