An absolute answer depends on your state law.
Generally, the person/company suing you has no legal interest in your car until they get a judgment against you and file a lien against your property (unless they are the car finance company or you voluntarily gave them a lien on your car). So if you transfer it before the case is over it cannot be attached by a later judgment lienholder.
However, anybody harmed by a transfer can get it invalidated under your state's fraudulent conveyance/transfer act. A transfer of property after a lawsuit begins would be a factor indicating that it MIGHT be fraudulent.
If you can show that the transfer after a suit is filed did not hinder the person/company's collection rights, the transfer should not be invalidated. Depending on your state law, you could show this in many ways. For example:
(1) the transferee had a legal interest in the property equal to what was transferred (i.e. when you bought it you agreed that it would be owned by both of you -- thus he had a pre-existing legal right to sue you for his half). This argument would be very strong if he paid for half, or his half was a marital gift (you gave him half because you love him), or you live in a community property state and it was bought with marital funds (money received after you were married). Even in non-community property states, the law may give a spouse an interest in property bought with marital funds.
(2) the person/ccmpany could not attach the car (check your state's exemption from attachment provision). If the car is exempt from attachment (which it is in many states) it is impossible to defraud the person/company by its transfer.
(3) When you transferred the car, you had other assets having a value that exceeded what you owed the person/company.
(4) Anything else showing the person/company is in no worse shape as to collecting than he was before the transfer. Check your state law.
Remember, if you transfer the car, it will require the person/company to file another court action (fraudulent conveyance/transfer action) before they can get your car. So they'd have to win the first case, then file and win another. If you don't owe them much, and/or they think you have a good defense to fraudulent conveyance/transfer, they may not even try.
Other input from FAQ Farmers: