Odolan Gurgul
Odolan Gurgul voted up Walt O'Reagun's answer
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.

Odolan Gurgul
Odolan Gurgul voted up Rooster Cogburn's answer
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?

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.