beam pattern—you need an angle vs brightness plot , hard to get and hard to boil down to one parameter
==not doable with phone easily
MAYBE by some kind of camera shot with controlled exposure parameters, plus using a white card and measuring/specifying distance from it

color temp—very hard
==MAYBE
would need some processing - MAYBE there is an app already but idk what it would be

total lumens is pretty hard
==not doable by phone
MAYBE by some kind of camera shot with controlled exposure parameters, plus using a white card and measuring/specifying distance from it
might get to 80% correctness