I am concluding from your query that you are coding for a Pain Management Specialist as opposed to an Orthopedic Surgeon or an Interventional Radiologist, neither of which is likely to do both of these injections at the same setting, and since neither should be doing Lumbar Epidural Injections at all.
Hip joint Injections can be done by Orthopedic Surgeons, Interventional Radiologists, and Pain Specialists, but not without radiographic (fluoroscopic) guidance. This is not an office procedure for Orthopedic Surgeons, who would probably refer the patient to either of the other two to perform. Also, the Hip Joint Injection is best approached from the front (anterior), which requires the patient to be on their back (supine), i.e. different positioning than for a Lumbar Epidural Injection. Therefore the patient has to be repositioned between each of the two injection procedures, plus the additional prepping and draping, and the positioning of the Fluoroscopic equipment for the second procedure/injection. In essence, these are two different procedures being done. This discussion may seem obvious or to be overkill to some, but it is important to know what is involved. So to answer your question, I would say yes to coding the Fluoroscopic Guidance (77002) along with the Hip joint Injection (20610), and Modifier 59: Multiple Procedure too.
I emphasize the word Joint in this discussion because injections into extra-articular soft tissues of the hip region (Trochanteric Bursa or a tendon, etc.) would also use the 20610 code, but these normally don't required Fluoroscopic Guidance. The "new thing" for these would be the use of Ultrasound Guidance for these injections, and usually these are office procedures by Orthopedic Surgeons.
Hopefully this helps.
Respectfully submitted, Alan Pechacek, M.D>