I suspect before buying hardware, you should write a program on your PC that can read two serial lines and displays the data you want in a format that would be similar to the LCD you plan on using. Write this in C or C++ and not higher level languages like perl/python/etc. This will tell you if it is doable. After that, I would buy an UNO, and see if it can handle the flow. If it does, you can then look at custom PCB parts using an AVR chip so you can get the cost down for the finished product.
If the UNO can't keep up, you probably need to step up to an arm. I tend to think the tweeny 3.0 which has multiple UARTs might keep up with really fast streams, and it has hardware floating point. Hardware serial ports tend to support signalling when they are ready to read data, so it is less likely you might have dropped data, which is important if the device just sends a full status report every minute or so. Obviously if there is a command to send just the data you are interested in rather than a summary of the entire machine state, that can speed things up.
There are many other ARM solutions, but you would probably need to carefully read the data sheet of the particular ARM chip involved. Even so, the most power reduced ARM is probably an order of magnitude faster than the AVR. Again, like with the UNO, you might start with a more expensive development kit, and then once you have a proof of concept, refine the design so it is cheaper and easier to manufacturer.