I checked the Broadfoot CD that lists all Confederate soldiers found in the records of the National Archives, and I do not find a record for a Lorenzo Parks (or Park)in a MO Confederate unit. Nor do I find a record for anyone of that name in a Missouri State Guard unit, the records of which are admittedly incomplete.

In the former there is a record for a Pvt Lorenzo D. Parks, Co G, 4th Ala Cav Regt, but I doubt that is the person that you reference.