As was said, you'd have to run your own lightning node, and integrate with a wallet like Zeus. The problem is that to run your own lightning node, you need a static IP address. Most people can't get this from their residential ISP. So you put it in the cloud on a VPS. But the problem with that is that to run a lightning node, you also need a full BTC node with an unpruned blockchain. That's over 500 GB and VPS cloud storage is about $10/100GB/month. So it's not really cost effective to do, and the only other alternative is to use a custodial lightning wallet like WoS or Alby. So, the thing to do then is only keep a small balance in that wallet and replenish it from time to time with a non-custodial wallet.
Discussion
Would a DDNS work as a way to direct to the correct IP? I have a DDNS already setup and a lot of storage space for a blockchain (though admittedly pruned would be better). If not then a domain isn't too expensive.
Domains are cheap. I picked up libertasprimordium.com from Google for $12/year.