Here is what MedNet New Zealand has to say about it:
Most lipomas are symptomless, but some are painful on applying pressure. Lipomas that are tender or painful are usually angiolipomas. This means the lipoma has an increased number of small blood vessels. Painful lipomas are also a feature of adiposis dolorosa or Dercum disease.
Another site mentioned that if a lipoma gets painful, the doctor can excise it. (Meaning, go back and see your doc and see if it can be removed.) Sorry, don't know what adiposis dolorosa is, except that dolor means sad and adipose relates to the fat under the skin. Sad fat? lol and I also know zip about Dercum disease. But something about the offhand way those are referenced makes me think they are not the most usual reason a lipoma gets painful. It sounds more like that too-many-small-blood-vessels thing. And if a doctor can remove it, why not. My husband has a lipoma on his back and I think it would be great if the doc would take if off, but the doctor has said there is no reason.