Well, I am no vet or vet technician, but I do know that lethargy, increased thirst, and weight loss, coupled with pale/and or tacky gums (this means that when the gums are pressed with a finger and the color doesn't come back, or it feels tacky like day old abc chewing gum), and skin tenting (that means the skin holds its shape after taking a fold of it and pulling it gently a little bit away from the body) are signs of severe illness. The tacky gums and skin tenting are signs of dehydration.
Really though, the vomiting could be something as simple as stress. Cats are prone to vomiting when super stressed. The color you described sounds to me like he is throwing up bile. That could be a problem. Continuous vomiting of bile tends to erode the esophagus over time (think of those heartburn and acid reflux commercials) and is probably not at all comfortable for him either.
I would at least call the vet and ask what he/she thinks. You don't have to take his suggestion of cat food (I know that vets usually are more inclined to peddle their own brands than the good stuff) and the chicken and rice food is really more geared towards dogs.
“The day the power of love overrules the love of power, the world will know peace.”
― Mahatma Gandhi