Matthias,
The solution of using the SPI port with a counter to generate the L/RCLK should work. You need to make sure you can align the L/R clock with the data using the reset pin in the application note you refrenced. Also please note on page 15 of the PCM1754 datasheet the LRCLK is used for synronization so becareful of jitter in this signal. Otherwise generating the LRCLK from a counter should be fine.
-Matt Kucic
Audio Applications