More than likely it needs a IAC cleaning or throttle body cleaning. MAF cleaning would also be suspect. When is the last time plugs were changed. Is the check engine light on. This car also has a timing belt. Has it been changed?
Timing belt and spark plugs were replaced earlier this year
also if it was a issue with misfiring due to a load on the engine it would also occur when the transmission was in reverse as this also puts a load on the engine considering the issue only occurs in drive on the lowest gear i am doubtful that its the engine itself because a misfire would remain noticeable at higher speeds if not prevent the car from accelerating properly it has also been in the shop quite recently for routine maintenance and no problems were found with the engine which is why i still suspect a transmission issue
Rough idle on an older car is usually caused by worn/collapsed engine mounts, especially on an old Mitsubishi. How old are the engine mounts? I don’t think new transmission fluid will help.
That’s a good diagnostic point you make OP that the vibration only occurs when stopped with brake applied at idle in forward gears D and 1, but not reverse. I’m with you, with no reverse involvement, it doesn’t seem like it could be an engine-firing problem. Except for this idea: If you had problems both with the engine and the mounts, it’s conceivable the vibration would be most apparent in forward gears, b/c the force the engine applies to the mounts is probably different in forward vs reverse gears. So maybe you have both engine and mounts problems.
I think @Barkydog 's idea, a proper transmission service, is probably a good place to start. What about the transmission fluid level? Does it check out ok?
Warm up the transmission/car. Engage the parking brake, hold the brakes and shift through all gears, then leave the car in neutral and then check the level on the dipstick. I don’t know why Mitsu has you check the level in Neutral and not Park, but that is the way they want you to do it.