I figured it out myself. Alby has it setup where I can receive Bitcoin and that is swapped to be used on Lightning.
Discussion
You can also use a non custodial wallet for maintaining a larger channel for random shopping. 1M sats is quite good figure, at least for me.
Running your own node is the best way to have a non custodial #Bitcoin #LN wallet although it needs you do some work.
If you can't run a full node, the second best thing is one of these:
https://blixtwallet.github.io/
No need to set anything up, the software manages everything. The same 1M recommendation applies, being non custodial means you can use both, the Lightning as well as on chain.