Can my bike have disk brakes fitted?
No  Those lugs are for mounting a rear mudguard/fender or a rear rack, not a brake caliper.

They are far too weak for a caliper, too close to the axle and would be torn off quickly by the leverage if you did somehow use them to mount a caliper.  

Remember that rear brakes are only 5-10% of your overall braking.  If you desperately want to add discs to this bike, either find a front fork with disc brakes, and a suitable front wheel with a rotor.

Otherwise you need to look out for a newer/better bike.