Can I remove a lipoma under my arm without surgery?

You assume that what you have is a lipoma but I would probably recommend removal to obtain a diagnosis as well as to remove the mass.  They do not go away on their own and tend to just get bigger.  I have seen people where the mass continued to grow and put pressure on the underlying nerves which can cause permanent damage.

It is very important to confirm the diagnosis of lipoma. Other masses like lymph nodes, tumors, cysts etc can look like lipomas at times. Make sure you consult a physician for making the correct diagnosis. If there is any doubt MRI would confrm a lipoma to great certainity.
Lipomas are benign. You can leave it alone and not have any surgery. You can have it removed by liposuction which is less invasive than open surgery.
Regards