When you say hard start I assume you mean it doesn't want to fire right away but the starter is spinning freely and able to illuminate a test light brightly.
If your car thinks it's running rich then it likely is, there aren't many things that can cause that.
-Check the air filter and clean it out(yes seriously)
-Check the MAF data PID(you expect to see about 1g/s per liter)
-Hook up a fuel pressure gauge and run the car, then turn it off. If pressure rapidly decreases you have a stuck open injector. You could also use a stethoscope on each injector, one stuck open would make no mechanical clicking.
-Check upstream o2 data; they sometimes go lazy with age.
If you meant the car thought it was lean, most often it's a vacuum leak. It's a 20+ year old car, I can assure you it has leaks, most are too small to make a noticeable difference until they get worse.
-All of the above applies.
-Check fuel pressure.
-Check for an exhaust leak, you may not hear it from inside the cabin.
You would expect to see a positive short term fuel trim on a cold start, followed by a slightly negative once warm; variance of +/- 10 is considered acceptable depending on RPM.
Since the car is stumbling from throttle input while trying to add fuel, personally I'd be going straight to the fuel pressure testing.
