Police say neither man was wearing a seat belt when the vehicle, going nearly twice the 40 mph speed limit, went out of control and hit a tree.
The Houston Chronicle reports James Cutliff filed the lawsuit in November.
Estate executor Gerald Treece said he hopes that the matter can be resolved fairly and with a settlement for the Cutliff family.
Treece described himself as being friends with both victims.
O'Quinn, who was 68, was known for taking on wealthy corporations.