Welcome to the forum! The Yamaha MG10XU mixer would be suitable to use with the L1 Pro systems.
If your TV only has an optical output (digital), you would need to use an audio converter to output from the TV into the mixer (which has analogue inputs). One example would be an optical to 3.5mm converter.
Does your TV also have an analogue audio output, e.g. 3.5mm headphone output or RCA?
I am using L1 Pro 8 for Karaoke and I can provide some suggestions. I have connected two Shure SM58 microphones on Inputs 1 and 2 using XLR cables. I am connecting either my Samsung TV or iPad Pro to get YouTube Kareoke music to Input 3 of L1 Pro8 via. Bluetooth. If your TV does not have Bluetooth connection, Fire TV stick is cheap fix to make it work. My friend is actually using Fire TV stream to YouTube music from his older Samsung TV to Speaker. If you prefer wired connection, you can connect tablets like iPad into 3.5 mm audio jack into L1 Pro8 and I guess sound quality will be better with wired connection.
I am not using any mixer as I don't need more than two microphones and number of inbuilt inputs and as well as available mixer features on L1Pro8 is sufficient for me in home set up. In fact I was initially thinking two L1 Pro 8 or one L1 pro16 but experts at Long McQuade and Sweetwater told me that would be overkill for most homes so I have only bought one L1Pro8 and it is indeed sufficient for large rooms. You may of course need mixer in professional set up but Bose T4S might be better choice.
I don't need more than two microphones and number of inbuilt inputs and as well as available mixer features on L1Pro8 is sufficient for me in home set up. In fact I was initially thinking two L1 Pro 8 or one L1 pro16 but experts at Long McQuade. MCDVOICE