Lipomas are usually just under the skin, but they can be locally invasive, meaning they are meshed with muscle or connective tissue. Lipomas can also have additional blood or connective tissue as part of the growth. These growths can appear anywhere on the body, but they are most frequently located on the belly (mid-chest and down) and upper legs.
Your vet may want to do a needle aspirate to further examine the lump and determine conclusively that it is a lipoma versus another type of growth. A needle aspirate is when a sterile needle is inserted into the lump and the plunger withdrawn, providing suction to collect cells from the lump. This is not painful, and not usually even noticed by most pets. Your vet will then place the collected cells on a microscope slide, stain them, and take a look under the microscope.
Once your veterinarian has performed a needle aspirate and is certain that it is indeed a Lipoma, most vets recommend a watch-and-wait approach. The lump should be checked at regular intervals, to make sure there haven't been any cellular changes. Large lumps, especially those under a limb or in another location to interfere with movement or function, should be removed as soon as possible.
It should be noted that there is a fatty tumor called a liposarcoma, and that is malignant. Metastasis is rare, but due to their nature (infiltrative) they are difficult to fully remove, and recurrence is common.
Step-by-step gallery of a lipoma removal surgery
(not for the squeamish).
Lumps and Bumps in Pets > What is a lipoma?