IF you only want to run 2 1K lights and
IF your dryer outlets has 4 prongs, it could be done.
you will need a dryer plug like this.
http://www.homedepot.com/h_d1/N-5yc1v/R-202647848/h_d2/ProductDisplay?langId=-1&storeId=10051&catalogId=10053
follow the instructions more or less except
I would only use a 2 wire cord without ground for the cord that powers the relay. you will only need a cheap timer to control it & most (timers) don't have a ground. the box and light cords will be grounded anyway.
run the red & black wires from dryer cord to the relay where he shows you to run red & white.
for the light cord, run the black wire to the relay's load terminal like he shows but only run 1 to each load side.
wire nut together the 2 whites from the light cords & the white from the dryer cord.
hope my 1/2 assed diagram helps.
>>>>>>>>>>>green---------------------------------------- greens from both plugs
dryer >>>>>> Red---------line1--pole 1 of relay -------------blk plug for light1
cord>>>>>>>>blk ---------line2--pole 2 of relay -------------blk plug for light2
>>>>>>>>>>>white ----------------------------------------whites both from plugs
not showing the coil side of the relay as it stays the same