Will Layer 2s talk with one another?

Hi Everyone, I’m just curious if ETH layer 2s can or will be able to talk to one another? Or will we have to connect to different L2s depending on the dapp we want to interact with?

For example, if a friend of mine starts using a loopring wallet and I use an argent wallet, will I ever be able to send ETH to his wallet? Or were L2s never designed to interact that way.

Thanks,