If the new employer is willing to apply for H1B with cap exempt, is there a possibility for me to change job?

I used to hold a valid H1B (approved I797 and Visa stamped). I got the visa approved for 9 months. But I couldn't travel on H1B with that employer as they hardly had any projects. My visa got expired in September 2015. Meantime, my employer in India applied for an internal transfer, so I am currently in US on L1B. I am planning to look for better opportunities in US. Will I be able to change jobs? Currently, I am on L1B I cannot change jobs. I read lot of post and blogs. They say it’s possible. Is it just theoretically possible or have many people done this? If the new employer is a bigger organization and have all correct documents will it be possible? Actually, I wanted to know, can I keep hope or should think my H1B is of no use? I should start all the way new with lottery.