The sound will only be needed while using the lifesize which is connected to the tv (the sound only). While using either Laptop or VDI, no sound is needed.
I figured out that I could use a DVI Switch only, because like you said HDMI and VGA both can be converted into DVI. So what about a DVI Switch with at least 2 inputs (Laptop and VDI) and 3 outputs (TV, PC Monitor and LifeSize) ? Any suggestions?
I would not use a bunch of converters, cheap switches, etc.. in a business setting where if it drops people that can fire you are sitting.
Look at an A/V intergrator, have them install proper enterprise equipment. Will be a few thousand for the hardware I'd say. From what I remember, the rack we used in one of our rooms was about $15,000 for the equipment and setup of it. I was not doing the setup but I was the lead IT tech and did a lot of the spec and some wire routing.