The lamp runs off dc, after the current from the transformer is rectified it comes out to be 24v at 1.5A going to the light.

How are you coming up with your numbers? 15VAC rectified and filtered is 21.21VDC, not 24. If the lamp is recommended for 15VDC and 3A then it's expected hot resistance (when fully lit) is, assuming 45W @15V that's a resistance of 5Ω. 21V @5Ω = 4.2A. 21V x 4.2A = 88W. Your transformer is not going to handle that much power.

 

Is this an incandescent bulb?
Why the need for DC?
Max.

 

We still don't know the technology of the lamp?, but I was faced with a situation with 12v (filament) yard lights, they usually did not last over our winters here, so I eventually found 12v LED lamps with a standard Edison screw base.
That did the trick AND a great deal lower current
Problem solved !
Max.