The data you provided (ulcerative colitis for 15 years, low grade dysplasia detected with colonoscopy) indicates the presence of precancerous changes in the colon.
Ulcerative colitis is an inflammatory disease of the colon (large intestine) in which there are repetitive inflammation areas affecting the colon surface. The affected mucosa undergoes a constant healing process during which the remaining healthy cells multiply in order to cover and heal the ulcer. However, this is a continuing process and certain of the cells might lose their multiplying control. This might lead to precancerous formations and eventually to colon cancer. The presence of precancerous lesions significantly increases the probability of developing colon cancer. The management guidelines tell that if low grade dysplasia is detected, then colectomy (surgical removal of the large intestine) is advised. Another option is to wait for another 3-6 months for another colonoscopy. However, a colectomy is preferred if the lesions are multifocal and confirmed by another pathologist.
No data can be found about the mean time of dysplasia lesions turning into colon cancer. All the studies can give is the percentage of patients in which colon cancer was detected in a 5 year perid after detecting the dyplasia. However, it might be important to you, that patients with low grade dysplasia are at a nine-fold increased risk for developing cancer than patients suffering ulcerative colitis while no dysplasia is detected.
I hope this information would help you in making your decision.