Arduino-powered silent relay needed. Will AQV210E work?
You are correct about driving it like a typical LED.  \$R=\frac{Vcc-Vf}{I}\$
Drive it with enough current (\$I\$) to cause the output to switch on fully (Looks like 1.6mA to 3.0mA is their max required turn on current.  They characterize it with 5mA though in the graphs).
For the load side, it can only handle 130mA, so do not exceed that.
Tick - Tock -Tick -Tock ... silence...