Correct me if I am wrong; I am basing my observations on pictures of your engine I have seen on the internet.
Your car has hydraulic lifters with the cams directly acting on buckets operating the valves. You do not have tappets one can adjust. The valve clearances are automatically adjusted via hydraulic tappets. You cannot adjust them. I am confused as to why there was a need for lathe machinist to get into the "tappets" to free them? If I recall correctly, cars with hydraulic lifters have zero valve clarences.
Has your cold start issue been resolved now that the lath machinist has "freed" up the tappets? .My guess is that you still have a cold start problem. Also my guess is that your cold start issue is caused by a fault in the fuel enrichment system (choke in old cars). It could be that at overnight the fuel line and fuel rail gets depressurized. This is normal. When the door is opened or when the key is turned or when the start button is pressed, the fuel pump comes on for a few seconds to pressurize the fuel rail. The car is cranked and it fires up right away. When the ECU sees low temperature from the temp sensor, it increases the injector fuel pulse duration by a few milliseconds to enrichen the mixture. We can see this by the engine running at a fast tick over. Once the engine warms up the fuel pulse returns to normal and the RPM drops to normal. It is this fuel system you need to look at closely and go from there.
