Go to home Depot and buy the WESTEK #6503B touch lamp unit [black box] not the screw in type!
open the unit and add the filters left out during manufacture!
install a few small ferrite beads on the sense line. some folks also add a 1/4w resistor ...anything from 680 to 1000 ohms and a 2.5mh choke. the intent is to desense the sense wire
go and replace the lamp cord with new stuff and use a polarized plug! of course wire the lamp socket and unit correctly...the outer case or the screw section of the lamp is neutral the tip of the lamp or center of the lamp socket is hot I add this to ensure other readers realize the correct polarity of the ac to the lamp and box! oh and the polarized plug....the narrow blade is hot and the wide blade is neutral
then reinstall the stuff and you should be ok. the older touch lamps are very sensitive to rf as little as 5 watts from a cb radio can trigger them.
re the alarm system...if it's a professional install let them fix it or you might have issues if you get robbed and the company says you tampered with the alarm!
but if you installed it do the obvious:
ensure all grounds and ac lines are correct [polarity etc]
check your cable run lengths did you make good antennas?
are your cables shielded?
have you added mix 31 ferrite split beads?
you get the idea