None. The lamp is rated for so many hours not whether it is intermittent. In addition by not turning the spec on and off you are reducing the 'wear and tear' on movable items like switches.
In my opinion, nothing happens. I was studying kinetics of the reactions with time ca. 24 hours and everything was good. Lamp after a half of hour is heated-up and then you can work. Spectrophotometers should be ready for such work and - as I know - lamps prefer a stable work. More destructive is switching on and off (even on a common bulb boxes you can find sometimes info that 'you can switch on and off this bulb for ca. 40000 times' or so). Only you have to sure that there is no other technical problem in your spectrophotometer and nothing happen because of other accident (thermostate, moving of couvette box, etc.).