Is it safe to get liposuction done if I might have chlamydia?

Maybe. You would be better off to get the chlamydia treated prior to undergoing any surgery, especially one that is completely elective.
No. It is not safe with any kind of active infection to get any surgery.
Get treated. Get tested and treated first...Never go into any surgery suspecting you may have an infection of any type.
Liposuction. I would agree with dr. Neilsen. Treat the chlamydia condition first prior to surgery.