How is a pilot guided laterally when using the HUD on takeoff since there is no FD?

There is flight director gudance cue with flight path symbol.

For take off you also can find: TOGA pitch target line and tail strike pitch limit for liftoff, HUD guidance cue and lateral deviation line for low visibility take off.

Read the HUD system description chapters in FCOM vol2.

I presume you're talking about the takeoff run. When airborne just keep the flight path cue within the reticule.

 

For the takeoff run, enter the runway data in the HGS panel (length, slope, elevation). Use primary hud mode. Tune the ILS for the runway. Set the runway track in the as the MCP course. Line up on the center line. You will notice a vertical bar, this is the rollout guidance cue. Keep that bar in the center during the takeoff run.