Lithium will work if no damage has been done to the bar that slides in and out of the door and the spring socket and the two steel balls that the bar uses to slide and catch with. Also if no damage has been done to the channel that the bar assembly rides in.
If the problem has just recently begun then chances are that no damage has yet occured and white lithium greese is your best bet. But if the problem has persisted for some time chances are that damage has occured and greese will not help.
1993 190E 2.3
2000 Toyota 4x4 Tundra