Just to add to what Parthery mentioned... Unless there's something new with the tranny that I'm not aware of, there is no way to 100% lockup the converter (at least there hasn't been in anything I've ever towed with - without special, aftermarket programming, anyways). Your converter will lockup at about 50mph under light acceleration (higher RPM's with higher throttle input). To you, it will feel like another shift. In other words, let's say you have 4 gears. If you note your shifts, from a standstill, you will feel 1 to 2, 2 to 3, 3 to 4, and then you will feel another one - that's your converter locking up (creates less heat when locked).
Now, let's say you're traveling at 60MPH - you have probably already noticed this - if you add a little bit of throttle (not enough to downshift - just "goose" it about 1/2"), you will notice one of two things. If the converter is currently unlocked, you'll notice the RPM's jump up faster than your speed. If you notice the RPM's move up consistently with speed, then the converter is locked. On my Sub, I can also tell by coasting and tapping the brake - if the RPM's drop to idle, the converter is locked. But this is on an HD 4L80 and I don't know if that works with a LD tranny.
Locking/unlocking is determined by some fancy-shmancy algorithm based on speed, load, gear selection, throttle input, etc. Keeping the RPM's a little higher (a lower gear than normal) will help to keep the converter locked up at a lower speed, where a higher gear would need to unlock to retain power.