When you conduct a web check in, there is an option where your boarding pass gets generated online and you can print out the boarding pass for presenting to the airlines staff before actually boarding your flight. So, this should be fine for the LTA exemption.
Now, if one was to consider the unfortunate situation where you had checked in online, but could not board the plane, then any verification of the boarding pass with the airlines in the event of a tax returns audit could land you in trouble, as their records would indicate a check in, but no boarding.
So, yes as long as you have actually boarded the flight, the boarding pass generated via web check in would be valid for LTA exemption, provided all other conditions of the LTA policy have been abided to.
Additionally wanted to check does the Income tax act say that web check in passes are allowed for LTA tax exemption