The lightning network is comprised of bi-directional payment channels between two nodes. This means that either one of those nodes should be able to initialize a transaction at any time. These transactions require both parties to be actively participating in updating the smart contracts that keep the channel alive. If one party fails to respond, they are essentially in violation of the smart contract, and are forfeiting their claim to any of the funds in the channel.

Non-responsive clients are a liability to anyone opening up a channel. It means that their bitcoin may be tied up in the channel until the timeout period. That bitcoin was typically put there either to make a payment (which now is delayed), or to earn network fees for being a hub of other people's transactions. An unresponsive node means the channel is wasted. It's similar to a denial of service attack, except it's tying up bitcoin rather than bandwidth.

I feel LN clients Would they have to rely on third-parties to commit for them when they're offline. The success would depends on how much reputation the third parties have built to be trusted . I'm thinking users would at least have to trust them to commit transactions in a timely manner to invalidate past transactions, right? This to me seems an awful lot of trust put onto third-parties