As said above the number of discs will not matter on when it locks up, however the torque converter itself can make a difference on when it locks up. There are different torque converters out there that behave differently. Some torque converters are setup, so that you actually have to lift off the throttle before they will go locked. These are often used in towing applications, so that the lockup won't knock cows off their feet.

A daily driver torque converter would normally be set so that the lockup won't happen until it's in OD, to save stock shafts. Unless, as previously mentioned, OD is locked out. The way my truck is setup now (with the valve body mods, and torque converter), under all but light acceleration, it will shift to 3rd unlocked, then go locked, then shift to 4th locked (it probably unlocks during the shift, but I sure can't tell).
A lockup switch can work well as long as you use it wisely...

A controller is safer.
My suggestion is that you contact the trans builders (I like DTT, but I have heard good things about the others as well), and tell them how you want it to shift, and let them make the recommendations on their setup. Doing a torque converter and a shift kit is probably not going to get you exactly what you want. Adding a controller will help, but doing a complete trans would be the best.
Paul