Just with Lightning, you would still be able to do that. You lock your Bitcoins in scripts which become Lightning channels, so they are stored there safely with Bitcoin's L1 guarantees.

If the channel is unidirectional and you are at the end of a Lightning "spoke", i.e. if you only use it to pay and not to receive money, then there is also no risk for the channel state to get "rewinded" to an earlier state. This means that in this case, there is no security tradeoff. Basically, you only "bundle your own transactions". If you open a LN channel with $10000 in it and pay $100 fees, Bitcoin is still competitive.

But even if you do participate actively in the Lightning routing (opining several channels in both directions), the security guarantees are still those of the Bitcoin consensus and you only have to monitor the state regularly to be able to initiate a channel close. There is no "middleman" like in the currently existing Ethereum rollups for example.