Does a photo-coupled SSR need a series resistor for the internal LED?
It varies depending on the SSR.

Really, every photo-coupled device will need some sort of current-limiting device, the question is just whether there is a resistor or some similar part built-into the SSR, or whether it needs an external resistor.



In this situation, the LCA710 is probably less accurately described as a SSR, and better described as a photo-activated MOSFET. You will need to provide your own current limiting.



In the datasheet, you can see they explicitly specify a maximum Input Control Current, as well as the Input Voltage Drop. If this were a traditional SSR, they would just provide minimum and maximum voltages. 

What the datasheet means when it says TTL/CMOS Compatible is simply that the current required to turn the FET on fully is within the sourcing capabilities of most common TTL/CMOS devices. Some optos can require upwards of 20-30 mA to turn on fully, which would prohibit them from being used with most common logic devices without an additional high-current buffer.

It's also worth noting that this is pretty much spelled out explicitly: the datasheet says Low Drive Power Requirements (TTL/CMOS Compatible). The critical part here is the "low drive power" bit.