There is only one file type that uses the .LRWEBENGINE extension:
Adobe Lightroom Web Gallery File
Photo gallery archive created by Adobe Lightroom, a digital photo editing application; saves a collection Web files that define how photos are displayed; acts as a plug-in for Lightroom and enables a collection of photos to be viewed.
LRWEBENGINE files are actually folders (packages in Mac OS X), so you can view their contents in Mac OS X manually by right-clicking the file and selecting "Show Package Contents."
NOTE: Lightroom was formerly known as Photoshop Lightroom.
Updated: May 8, 2017