I believe the answer is definitely no. The standard barrel will not fit the light weight version of the Browning A-5.
What makes the lightweight different is that they have removed small amounts of metal in certain places, including the barrel. If you look at the lightweight barrel, you will see that there is a square hole cut in the rear of it, and I guess that this is part of making it lighter.
I would suggest that you may want to re-state your question on the Gunsmithing Board, as you will probably get many more replies.
Best Regards,
Mannyrock