We also had mice models of Parkinson's disease and checked if the deficits produced by neurotoxins were reversed by daily wheel-running. It seems that L-carnitine may play a role in the treatment of Parkinson's disease :
Article Combined R‐α–lipoic acid and acetyl‐L‐carnitine exerts effic...
I have not seen a trial with specific intervention of L-carnitine for PD but there are at least two trials in which Asetyl-L-carnitine is one of the components of the intervention:
1. NCT00903695: RCT with 10 patients with results: (Terminated before end because risk/benefit ratio did not indicate further study would be useful, or fair to future subjects.)
2. NCT01320527: RCT with 135 patients completed trial and if you search the trial number I think there are some published reports of the results.
Here are links to trials register if you are interested in details of trial and contact details of researchers: