Going to Lakes doesnt promise a career with a major. Major's havent hired in great numbers for years. The guys that usually go to the top of the list are Military guys that already have heavy jet time with international experience or Corporate guys that flew GIV's or a Global Express.
Can you go to a major from GL sure, but the likely hood is actually pretty slim. Alot of the majors are trimming down and regionals such as RAH are getting alot of the Mainline routes. If you go to Lakes dont bank on a Major to follow. Build your time and take the next best offer whether it be corporate/airmed/or a better regional.
I took a job flying cargo in a BE99 then a 1900 and still haven't been picked up by any major. I am however VERY happy with what I do. I fly 2-3 days a week and paid very well granted I fly for a private owner.