Yes, but not at ludicrous speed!

Relevant

No. From the perspective of a theoretical car driving at lightspeed, the beams of light would never project ahead of you. In reality, any object of mass that reaches the speed of light would be converted from matter to energy, so the headlights would cease to exist

The light from the headlights is travelling at the speed of light anyway, so I would’ve thought that of course you’d see the headlights What you might be meaning is, if a car, for example, was travelling at the speed of light with its headlights on, and if you were an observer stood in front of the car, would you still see the headlights? Again, I don’t see why not. Light travels at around 186,000 miles per second and we always see it under normal conditions. So if the lights are on a vehicle travelling at 186,000 miles per second, then surely we should still see the lights Maybe someone with a physics degree could clarify

Assuming a spacecraft with mass could travel at light speed (which it couldn't), I would assume no, because the ship would be moving just as fast as the photons themselves. Also, physics and time get real weird when you're approaching c, so I don't want to speculate too much. I assume you're also a vsauce fan?