Alexa does have the ability to limit a routine to specific days and times, and if you’re just turning on lights that may be enough for some people.
The other thing you can do is move the complex logic to the ST side. Have an Alexa routine that triggers from a Ring sensor and turns on a virtual ST switch.
Have that virtual switch coming on trigger the light coming on in ST, but only if all your other conditions are met.
But you would have to have another set of routines that turned on yet another set of virtual switches that were proxies for Ring armed state.
So it is doable, but clunky and cloud based.
I know turning on a light when the alarm is triggered is a frequently requested improvement for Ring: hopefully they will add it along with integration options in the future.