If Lecter is also a criminal then why did the investigation team trust him in The Silence of the Lambs?
Why would a criminal give correct information about another criminal?
For the challenge it presented to Lecter.
Lecter used to consult for the FBI, and it's implied his services were largely au gratis, and often pro bono.
Whilst it's true that he often manipulated his proximity to the FBI for personal leverage, he seemed to genuinely enjoy the pursuit and capture of criminals.
Knowing this is something he may willingly participate in (coupled with the prospect of improved facilities and privileges), the only reason Lecter wouldn't help is to be spiteful, which would in turn only spite himself.
It helps to know that the book is inspired by real cases:
Thomas Harris was moved to write the novel that inspired the film after meeting FBI agent John E. Douglas, one of the godfathers of criminal profiling. While attending the lecture of the decorated special agent, Harris learned about three notorious serial killers: Ted Bundy, Gary M. Heidnik and Ed Gein.
Of particular interest is Ted Bundy:
And like Lecter, Bundy had an interesting relationship with a criminal investigator. His contact was Robert Keppel, a homicide detective who had achieved national attention as being one of the men who had helped track him down in the midst of his cross-country murdering spree. Keppel was serving as the chief consultant to the task force for the unsolved Green River Murders when he was contacted by Bundy from his Florida holding cell; Bundy offered to help form a profile to help catch the Green River Killer. While working with Bundy ultimately provided little help, Keppel was able to get him to confess to several more unsolved murders. Bundy was executed in 1989, while the Green River Killer -- Gary Ridgway -- was finally apprehended in 2001.