A custodial lightning provider could shut down and walk away with user funds at any time, so it's still an IOU. It's theoretically possible that a custodial provider could mimic a fractional reserve system by having more IOUs issued than total liquidity they have available. It is something to be concerned about.
To have bitcoin on the lighting network, in a custodial wallet. Are you said to hold the bare asset?
Discussion
These are good insights