What is the name/cost of the procedure to remove underarm fat and side boob?

It sounds like you need liposuction and excision of skin to the area just lateral to the breast, often referred to as an axillary roll, or lateral chest roll.  I often try to include this as part of my breast reduction, but it is cosmetic, and not part of what insurance will pay for.  It only adds an hour or two to the case, but it's definitely worth it.  

So, since you've had a lift already, it's possible that the incision would extend around to meet your vertical/lollipop incision - I often extend this incision around as one.  It helps tremendously, and looks fantastic, provided you can accept a scar.  Without pics it's tough to tell exactly.

It's really hard to accurately answer your question without either photos or a physical exam, but I will try.  It is not uncommon for women with very large breasts to also have a roll of tissue that extends laterally under the arm, just past where the edge of the breast ends.  I call this an axillary roll.  I often address this at the initial breast reduction procedure either by doing liposuction (if the skin tone is good and I can expect a smooth contour) or by directly excising the excess fat and skin (if the skin tone is poor).  The same principles can be applied to secondary correction.  If the tissue is directly excised, the incision is planned so it lies in the inframammary fold and is very inconspicuous.  I hope this helps, and best of luck.