I also have high lymphocytes, not double the normal but still way out there. I was sent to an oncologist for a workup, and the guy ordered some very sophisticated tests to determine the exact nature of my lymphocytes.
It turned out they were benign. People can have an elevated lymphocyte count in response to autoimmune conditions, one of which I have.
On reviewing my previous blood work, we found that I had had high lymphos for at least 13 years, and one doctor had just suddenly noticed it! My diagnosis was 'atypical lymphocytosis,' which you can google.
My oncologist says, based on my tests, there is almost no chance my condition will turn into leukemia, but since it theoretically could happen, I should have blood work done every couple of years.
Hope this helps.