I'm not in the bike industry, just a consumer. But here is one approach that might work for the LBS to compete with the online sellers. I can't see how this would work for parts, but possibly for complete bikes.
So a customer comes into the store and says "You want $2000 for a Stinkbike 2000 SUX. I can get it online for $1500." And sure enough, he can. And you have one in stock that cost you $1400 which is already assembled and on the sales floor. They are still available from your distributor, too. If you sell it to him for $1500, you might even lose money with the time invested in assembly, etc. But walking out of the store today with an assembled bike is not what he would get if he ordered it online.
So order him one from your distributor. Charge his credit card $1500 the minute that the bike ships from the warehouse. When it arrives, turn the bike over to him in exactly the same state that it would be if he ordered it online. If that is in an unopened box, then fine. If that is partially assembled, bring it to the same level but no further. If the manufacturer didn't true the wheels, resist the urge to tweak them up. Do not provide the customary fitting, tune up, or free adjustments; if he needs any of these he'll have to pay your normal rates. The same goes if he doesn't have his own tools for assembly. And he has to get rid of the cardboard box, too!
If there is a warranty issue, he needs to remove the defective part, pack it for shipping, and pay the shipping costs. If the mfr pays for shipping, then this may let you ship it back to the customer with no $ out of your pocket. He's on his own to reinstall the part, or you do it at your normal shop rate.
If you put a shop sticker on the bike, have one made that is a different design for the price matched bikes. Your staff will then know not to do any free or discounted work on the bike. Or just don't sticker it at all.
I realize that your agreement with the bike manufacturer might not let you do the above, either. And you run the risk of a disgruntled customer telling his friends only 1/2 of the story; that your shop didn't assemble his bike. So there is a downside.
Just my thoughts...
Edit - And have a lawyer come up with a big, long list the terms and conditions (to include your standard shop rates) that he as to sign when he orders. That way he can't say "I didn't know."