No ! Once the van has been sold on a lien, your name has nothing to do with it any more. They got their money. You owe nothing.
If they sold my vehicle back to me in a lien sale from towing co. that picked it up down the road after it was stolen from a storage park that I owed some late fees to. Will I still owe those late fees that incurred before my van was stolen after I buy it back in the lien sale from the towing company?
Chances are ... The lien was from the towing company, for the tow and storage at their yard - and had nothing to do with the late fees from the storage company you had it at before. If that is the case, then - yes, you still owe the storage company those charges.
You rented the space, you entered into a contract to pay for the space .. You got the space, you used it, you still owe for the rent .. If the vehicle was sold to cover the cost of the rented space, then what they got for it would be applied to your bill.