By LCD I'm assuming you mean a panel on the back of the camera, and by through the lens viewing, I'm assuming you mean something you hold close to your eye and look through, much as you would do with a dSLR... A few mirrorless cameras have rather lousy optical viewfinders, but most have electronic viewfinders, or LCDs, or both.
All of the "dSLR form factor" and some of the higher end "rangefinder form factor" MILC or DSLM or EVIL cameras (That's Mirrorless Interchangeable Lens Camera, or Digital Single Lens Mirrorless, or Electronic Viewfinder Interchangeable Lens, all common acronyms) have electronic viewfinders. The dSLR form factor cameras tend to have the best implementations of EVFs.
Better mirrorless cameras with an EVF can be programmed to display several different screen layouts on either the rear LED/OLED LCD screen or the EVF. Many have sensors near the eyepiece that automatically switch the view from the rear screen to the viewfinder as you move the camera up to your eye.
The link Linda listed is an excellent description of mirrorless cameras and their technologies.
I would look carefully at Fujifilm, Olympus, Panasonic, and Sony mirrorless gear before buying. Each company makes very different cameras, each of which has a good niche in the market. You can watch all sorts of camera reviews on YouTube, and read in-depth reviews at
http://www.dpreview.com. If you plan to buy one, see if lensrentals.com or borrowlenses.com has it available for rent. Try before you buy. The interfaces are all different!
By LCD I'm assuming you mean a panel on the back o... (