Could a checklist app result in lawsuits if it leads to OCD?
For example, one might have a checklist for leaving the house. This may give you some comfort at first but may eventually lead to OCD.
There are potential tort liabilities. Each jurisdiction has its own rules of law for that. An understanding about "proximate causation" will put you on the path to assessing your own tort liability risk.
A study of contracts in your jurisdiction is needed to assess your contract liability risk.
Every jurisdiction has its on strict and products liability laws, so you need to learn those, too.
Further compounding your issue is what jurisdiction's rule of law applies? The facts and the lawyer's skills will determine how that plays out.
So the answer to your question is, "It depends."
A well written terms of service for your application should include legalese to cover liability for use of the service ("you use the software at your own risk, you don't hold us responsible for damages due to use of the software, no expressed warranty, etc"). You're probably ok just using a sample terms of service if you are solo or small, but you will want to talk to an actual lawyer with experience in this stuff when your business grows and you start making significant money.
Disclosure: I build legal case management software for large organizations, so I'm not a lawyer, but I am familiar with the kinds of things that companies get sued for (everything!).