Breez is non-custodial and would allow you to send sats, but it wouldn’t give you a lightning address to receive them. (You’d have to generate an invoice or receive on-chain.) They’re testing a service called “Breez Cloud” which apparently will allow users to run their own nodes on a cloud service.
Discussion
I used to have Breez Mobile and a Bitcoli account, which gave me a non-custodial wallet for sending and a custodial wallet for receiving. Having to periodically transfer sats from Bitcoli to Breez was a hassle, though.