Help a noob understand: Are rollups analogous to the lightning network for Bitcoin?

I just finished studying up on the lightning network for Bitcoin and it is awfully centralized/trust based in my opinion.

For Lightning:

1. You need to run your own node which has to always be online for you to send and receive payments. If your node goes offline your payment channel counterparties could close your channel and steal the funds on the bitcoin blockchain: this happens by them submitting old transactions that have the bitcoin balance be favorable towards them, ignoring later TXs. so your node must always be online to make sure your channels are honest.
2. You also need to backup your channel states. If you lose these, you end up having to TRUST your channel partners, again, to be honest.

HOW DOES THIS RELATE TO ETHEREUM?

Self-running LN nodes is not a solution for a lot of people. This will make it so everyone uses an easy phone app to use Lightning Network and trusts the app developer to handle all the node behavior for them. Essentially wiping the trustlessness of Bitcoin. Most users on LN do NOT have their own node. Once enough funds have been controlled what stops a node provider from stealing Bitcoin? Users which do not run their own node will have no recourse. These full-service lightning services are trusted LOT more than a user on the actual bitcoin using a wallet app node to broadcast a transaction.

Based on my understanding of rollups you are also trusting those that close the rollup data on Ethereum beacon, to be honest. Does that mean everyone using rollups should also be running their node to make sure the rollup providers don't broadcast bad TXs? Or can normal users be as hands off when using rollups as they are when using Ethereum?

I appreciate the help.