Delay lighting switch
If you really mean that all the lamps are wired in series, then what you ask is not possible.  One way or another you need individual control over the lamps, since you want them each to do something different.

If you just mean you want the bulbs to come on in a seires, then have the switch turn on a microcontroller.  This waits a little while to make sure the switch is really on (debouncing).  It then turns on a sequence of relays.  Each relay switches the power to one bulb.  The timing between enabling the relays is done in the firmware, so can be as flexible as you want.