I bought a Lenovo Ideapad 110 at an auction and it is password protected. How can I do a factory reset without having a password?

Contact auction seller for any information if they have it. Or contact Lenovo about what to do. We don't know you or accuracy of your story, so that is only what can be recommended here.
Answers should not get involved with password questions because of legal and personal security issues.

With your receipt from the auction, a local technician can do this. The result will have only the operating system on it and then only if the product key label on the back still works. You should expect that it will take a week or more… Tech will have to get some materials from Lenovo.