You probably won't be able to find out if there are liens on a mower. Typically financing for power equipment is an unsecured/signature/revolving credit. That is, a person is given the credit and the item being bought is not considered collateral (like with a house or car). If somebody sells you a mower that they still owe money on, it is on them. Just like if you buy a used TV that somebody bought with a credit card. If the original purchaser fails to pay their bill, that has nothing to do with you.
As far as buying potentially stolen merchandise, It is pretty much up to you to determine if the seller is shady or not. AFIK there is no national database for stolen items. If you have a contact at your local police dept you might get somebody to check for you, but if that item was stolen somewhere else...