My 11yr old has a lump in her left breast?

It's fairly common : For a girl to have a unilateral "breast bud" under the nipple & areola at her age. Sometimes it can be sore from being a little inflamed. If it really bothers her or is in an unusual spot, let her pediatrician check it out. Generally, it requires no treatment.

Congrats! Puberty: It certianly sounds like pubertal changes breast tisuue can begin anywhere in the breast area during puberty - it does not have to start right under the nipple. Tender is good too, although she may not think so. It's the non-tender breast masses that would be of more concern. And usually one side starts before the other (usually the dominant hand), so the fact it's just one side is ok to start.