If we're talking lumber as in, boards milled in Canada (BC) then there might be some benefit to us. But if we ship raw logs we also ship hundreds of jobs away from our families, really good paying jobs gone, from Canadians. Chile has sent us 'good one side plywood' made from our logs. 
BC used to make the best plywood in the world.

I grew up in BC and watched with horror the devastation caused by Campbell's selling off our most important govt. assets, Dept. of Highways, Workers Compensation Board etc etc. 
Including the 'fast ferries fiasco' that was never properly explained to the people of BC and was used falsely and underhandedly as bludgeon against the BC NDP and the people of BC. 
All done for power and not to help BC, just for the votes!

Recently I watched a 200ft super tug haul three very large barges daisy chained and  loaded double wide with BC logs.
Why didn't we send lumber boards instead?   Profit. Not sustainability, profit.