Are there general guidelines for LiPo discharge current?
Discharge is rated in &quot;C&quot; for example if your selected battery states 20C the maximum discharge is 20 * Battery capacity.
One of the reasons LiPo batteries are used in RC projects is the fact they can normally handle a high C rate (They can deliver a punch to the high-power motors).
If we look at the two options, you provided
Panasonic CG-320 - I've found a more detail breakdown of its specs here - LINK
The highest diagram they shown details a max discharge of 1C, they also mention in the handling guidelines to not let the battery voltage drop below 2.7V so you may need to do some voltage monitoring to be safe. Annoyingly thats the only mention I can find of discharging, so from that you could possibly assume the max discharge is 1C.

The 70mA Battery you linked has basically no technical documentation I'd recommend looking for a better documented version. Without a datasheet its impossible to know whats safe.
A better documented alternative would look like this Farnell LiPo this part has a datasheet with all the info you need here - Datasheet. I would recommend looking around the high end suppliers, Digikey, Farnell, RS &amp; Mouser they generally require suppliers to provide proper technical documentation.