No, not really possible. Even if you used a +5vdc to 110vac inverter the power available from an Arduino is less then 2.5 watts so that wouldn't light a very big lamp. Much more practical is to use a solid state AC relay or a plain relay that would interrupt the normal 110vac wall current to the lamp.
You need to explain better why you don't wish to use a 110vac wall outlet for the power source for the lamp. If this is for a portable application where no power is available then you would need a more traditional AC inverter powered from a large 12vdc battery to generate the 110vac for the lamp.
Lefty