If you use the Lynx PCIe card, than you would not be able to use the Tascam Firewire option or at least not be able to use at the same time.
If you don't need to mix while recording, I would likely not use the mixer. Just go mic-mic pre-Lynx-DAW software.
You can only use the Mixer features such as the effects, eq, compression if the audio is going through the mixer and most of the time all the mixer features except the analog inserts are all post A2D.
I have not spent much time with the eq or compression or effects as I have only had the mixer for a few weeks and I also have a lot of high end outboard that I would rather use, but from what little I have fooled with it, they all have surprised me as being decent and useable that is also pretty quick/easy to use.
So in addition to freeing up rack space from the non required patchbays, I also removed my two RME Digifaces and Alesis AI-1,
What you need to decide is if you wil be mixing audio in the PC or in the mixer. Or both, which is an attractive option to be able to have in my mind
Using a digital mixer as a DAW/MIDI/MMC controller for mixing in the box ignores most of the mixer features (because it is a mixer first) which may bother some people for paying for more than what you need. It used to bother me enough to not buy one until the Tascam showed up. Even then, I waited more than a year to see what issues and updates it had. The outcome was that I thought it was worth taking a chance on.
If the digital mixer has everything that you need as a mixer and/or a controller for the price your willing to pay, as in my case, then the exra features that you do not plan to use it for are a bonus. You may never need to use them, but I think you will find down the road that having those features available to you, you will soon find ways to make use of them.