The LS-AES is a companion card that provides 8-channels of AES/EBU digital I/O to the LynxTWO or L22. Your store was correct, you would need AD/DA converters as well to connect to an analog signal source.
Is the Triton and your pre-amp the only devices you're concerned with? If so, doesn't your Triton have Digital Outputs? The L22 has Digital I/O that can operate as AES/EBU or SPDIF. Even if the Triton only has SPDIF Optical, you could use a format converter to end up with SPDIF coax or AES. This would allow you to record the Triton output digitally, and you can even monitor it through the L22 analog outputs.
If you need to connect more analog devices, in the near future you will be able to add an
Aurora to the L22 for 8-channels of analog I/O, without downgrading from the sound quality you're getting through the L22 analog I/O.