As you can not connect directly to the Lyr using S/PDIF.
Using RCA to RCA from the STX to the Lyr is going to be the best possible direct connection.
Using the STX's RCA output bypasses the STX's headphone surround sound, so the RCA outputs only provide basic 2-channel stereo audio source (which should provide great music audio).
Low cost "Premium" RCA cable.
http://www.monoprice.com/products/product.asp?c_id=102&cp_id=10218&cs_id=1021814&p_id=5346&seq=1&format=2
In the future, you could get an external DAC, connect the STX to the external DAC (Bifrost?) using S/PDIF (optical or coaxial) and use RCAs to connect the external DAC to the Lyr.
This way you could still use the STX headphone surround sound features.