Blink is a good custodial wallet.

If it's already onchain you will have to do a onchain tx to the new wallet, this is most of the time cheapest on Sunday/Monday morning. If it's too expensive to move the fund you can only wait for cheaper fees.

Blink can receive/send both on chain and lightning.

If you want to store bigger amounts with less risk than custodial ln you can swap to liquid with boltz and use the Blockstream Green liquid wallet.