When I turn my head it feels like there is some loose skin under my chin - Is a Neck Lift needed? (photo)

There is definitely some loose skin, but to suggest what treatment would be helpful, an in-person exam and or some further views would be needed, like a frontal view relaxed and grimacing to evaluate the platysma.
Treatment depends on how loose it looks and if there is any concern other than when the head is turned.
There are skin tightening modalities both external and under the skin, available, as well as lasers for texture and tightening.
A current minimally invasive non-incisional option for necklift is MyEllevate. This is a necklift without an incision done by placing a suspension suture under the jawline from side to side using special instruments and tiny punctures to move the suture with a light rod to which it is attached. These punctures do not leave a scar. Recovery about a week.

A little platymaplasty (neck tuck) would tighten up the loose skin nicely and easily for roughly $8500 for quality work. Nothing else will make enough of an improvement to try. It is done under local and has dramatic results.

Thank you for posting your question here !my answer will be based on the limited information and pictures provided , for a detailed and personalized plan please consult with your plastic surgeon in person.
you have many options and the the ultimate choice will depend on how invasive of a procedure you are willing to go for , it does appear that you have some redundant skin , but it is hard for me to tell for sure just based on the pictures provided there is a chance that what i am seeing is platysmal bands and if that is the case a neck lift or botox injections could address that issue depending on how invasive you want to go. If it is just redundant skin then you can try less invasive modalities like radio-frequency microneedeling , ulttherapy or even renuvion for less invasive measures your issue is still mild that you might find good results with those modalities . A neck lift would address those issues but everything is a tradeoff and you will have to be willing to undergo a more invasive procedure with some scars ( relatively well hidden but still present).I hope this helps!, best of luck!