I suppose lightning transactions initiate smart contracts

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Yes. Lightning channels are smart contracts on Bitcoin in a 2:2 multisig.

Multisig means both parties must sign the transaction before the UTXO is spent?

Indeed, and they do so every time a Lightning transaction occurs on the channel, they just don't broadcast that transaction to the blockchain unless and until they want to close the channel.

And 2:2?

I got this. 2 keys are needed

Thanks, buddy!