Very, very hard. Many of us do intense sprint and heavy lifting workouts regularly.
It's normal to feel low on energy for the first several weeks of eating low-carb. I had a rather severe case of the so-called "low-carb flu" but continued with my intense workouts, and it didn't hurt me a bit. Having half a piece of fruit with some almond butter first helped.
Others wait until the weak phase passes before working out hard. Either way is probably fine.