There are no "lifters" in this engine. The cam acts on the rocker arm. which rests on a ball stud on the outboard side of the head. The ball stud contains a hydraulic mechanism which holds the rocker against the cam lobe thus keeping it quiet. These are called "hydraulic lash compensators (HLC's)."
It is not clear from your post if these were replaced.
I just did a cam and ball stud replacement in my 380SL, and it is very important that the pre-load adjustment to the ball studs be done if any of the components are changed. This is basic stuff and you should find a mechanic familiar with this process.
If the engine is quiet when warm, the adjustment is probably OK or close to it. However, it does sound like you have a defective HLC that is losing its hydraulic pressure ("leaking down') when the car sits. Your mechanic may be able to identify it by allowing the car to sit and then checking each rocker arm for looseness by rotating the cam.
I did a post on this that included Herr Fuch's "finger test" for finding bad HLC's.
Falls Church VA
'66 200, '66 230SL, '96 SL500. Sold: '81 380SL, '86 300E, '72 250C, '95 C220, 3 '84 280SL's '90 420SEL, '72 280SE, '73 280C, '78 280SE, '70 280SL, '77 450SL, '85 380SL, '87 560SL, '85 380SL, '72 350SL, '96 S500 Coupe