A Rune-style cross-chain DEX secured by Eigen AVS

In Thorchain, we need to provide RUNE plus some value assets like BTC and ETH for LP on their cross-chain DEX.
Is it possible for us to build a ETH L2 that do the same as Thorchain, but this time you only need to provide ETH plus BTC/AVAX/SOL to do LP, using Eigenlayer active restaking services for validator set?