Sections 2 and 3 are linked via the dog clutches (nothing to do with the main clutch controlled by your left pedal) of each gear. So when you are sitting parked with the engine idling in neutral, the engine is driving sections 1 & 2 but not 3, because none of the dog clutches are engaged. Then when you step on the clutch, section 2 will continue to spin under its own momentum until friction slows it down (or if you attempt to shift into any gear). Then only section 1 will be spinning.

The whole idea of LC2K is to synchronise section 2 with the speed of section 3 to enable easier shifting and preventing wear and tear on the synchros. I'll use shifting from 5th to 3rd as an example.

Single Clutch steps: You're driving in 5th gear, and you want to downshift to third.

1. Release throttle and step on the clutch. This disengages section 1 from section 2 and 3.

2. Move the lever from 5th to neutral. Disengaging gear when the clutch is disengaged is easy and doesn't cause wear to the gearbox.

3. Shift from neutral to 3rd. When you attempt to shift into 3rd gear, the speed between the 3rd gear + output shaft (section 3) and the lay shaft (section 2, spinning under its own momentum, because the clutch is disengaged) is different, so the dog clutches won't engage. That's where the synchros come in. As you push the gear lever into 3rd, the synchros engage gradually, and cause section 2 to spin faster until it matches the speed of the section 3, then only can you engage the 3rd gear's dog clutch.

4. But now section 1 is slower than sections 2 and 3 (spinning together, because you've already engaged 3rd), because you've released the throttle so you need to step on the accelerator, rev match and...

5. Release clutch for a smooth gear change.

Compare this with LC2K:

1. Release throttle and step on the clutch.

2. Move the lever from 5th to neutral.

3. Here's the difference. Release the clutch, so that sections 1 and 2 are engaged and spinning together. As you are in neutral, section 3 is still spinning independently from sections 1 & 2.

4. Rev match so that the speed of sections 1 and 2 and matches with section 3.

5. Now all three sections are spinning at the same speed. Step on the clutch, this disconnects sections 1 & 2. Because sections 2 & 3 are now matched and synchronised, it's easy to move the gear lever into 3rd, there won't be much resistance as the synchros don't have to spin up section 2 as in step 3 in the single clutch shift.

6. The instant the 3rd gear's dog clutch is engaged, release the clutch.

There may be an extra step involved but this downshift (if done correctly) will be noticeably smoother than a single clutch downshift and you've saved wear and tear on your synchros.