I have no experience with the Browning Lever Action, but I do have a similar rifle, a Winchester Model 88 Lever action in .308.
These guns operate on the same principal in that they are more of a lever actuated bolt action, than they are a true lever action weapon. This enables them to fire modern high pressure cartridges like the .308 and Magnum rounds. Both the Winchester Model 88, as well as the Browning BLR are capable of very good accuracy. Mine routinely shoots even inexpensive ammunition at or under 1 MOA. The Winchester Model 88 fell victim to high production costs with it's all steel receiver, and many hand fitted parts in it's intricate action. I would not hesitate to purchase a well cared for Browning BLR as these guns are very desirable. Bill T.