Lindsay Lohan -- Pisses Off Prosecutor ... Greeting Fans Doesn't Count As Community Service!!

Lindsay Lohan shook a bunch of fans' hands after her play in London, and thinks that should count toward her 240 hours of community service -- but prosecutors say NOT SO FAST, LiLo.

Lindsay's attorney Shawn Holley showed up in court Wednesday morning to submit proof of Lohan's community service progress ... which showed she managed to pull off 80 hours in just 9 days.

The City Attorney said some of the service looked hinky ... because it included time spent doing meet and greets after her play. Holley pointed out the previous judge in the case had approved the London facility that keeps track of Lindsay's community service.

The City Attorney isn't satisfied with that ... and demanded 2 weeks to investigate exactly what Lindsay did or didn't do to complete the 240 hours.

As for the mysterious chikungunya Lindsay supposedly picked up in Bora Bora ... Holley presented a doctor's note that she had an illness, but we don't know if it's the tropical virus Lindsay claims to have.