Critique my (possible) new system. Suggestions welcome!

For video processing? I’m not sure I can connect everything through the Lyngdorf without the add on HDMI module which I do not have. I guess I’m not really sure to be honest. I figured it would be easier to keep the Yamaha and have all video components run through that, keep some flexibility for the future if I added a center channel or surrounds and let the new stuff handle the music listening. The AVR is only a year or so old but I’m still learning about all of this stuff. 
What would you suggest?

If it's  fairly  new and you might add more speakers then I would keep it and use whatever new integrated amp you have for the l and r front and let the Yamaha do the res. Makes sense if you plan on adding surround  you only mentioned 2.1 in your original  post. 

Ya I would nix the A/V receiver and run your video sources direct to the tv and their audio into the Lyngdorf. Keep it simple. Think about adding a second sub configured for stereo. The idea that deep bass is monaural is not true. Also introducing bass from a second location usually evens out the bass response in the room. Try to put one sub near each speaker. One other tip for better imaging is to cover the TV with a heavy blanket when listening to music. Having a highly reflective surface between the speakers can mess up their ability to create a 3 dimensional image of the performance.
You will be surprised how good an experience can be had with a two channel theater system. Much simpler and less expensive.

I’m not sure I can connect everything through the Lyngdorf without the add on HDMI module which I do not have. I guess I’m not really sure to be honest. I figured it would be easier to keep the Yamaha and have all video components run through that, keep some flexibility for the future if I added a center channel or surrounds and let the new stuff handle the music listening. The AVR is only a year or so old but I’m still learning about all of this stuff.
What would you suggest?

Yeah no sorry I misunderstood, thought you were bypassing the Yamaha and using only the integrated. A/V receivers are the very bottom of the audio barrel. I would look at selling it asap. See if you can get enough for Total Contact or a decent interconnect, or power cord, anything will be an improvement.
I'm not kidding. You have an integrated. You have the Yamaha. Set them up and compare side by side. Use the same power cord and interconnect. If its not obvious the integrated sounds better I'll be shocked, apologize, and STFU!
This is what I do- run the video via HDMI cable direct to your display- projector or whatever it is. Run the audio RCA direct to your integrated. If you want to use something like a laptop, which I do a lot, simply use a whatever-it-is to RCA adaptor. With my MacBook Pro I also use an HDMI adaptor. This is by far better audio AND video than you can get by going through an A/V receiver, AND it saves on connectors. Plus you can if you want use a quality RCA interconnect for much better audio with your movies. Which will sound much better with two good speakers and two good channels of amplification than five or whatever cheap ones. Its not even close.

But hey, don't take my word for it! You have them right there. Compare and see for yourself!

Room acoustics before cables.