Note that LCD controller and Cura agree on motion direction. + and - of each axis works equally well in the LCD and in OSE Lulzbot Cura. LCD control is relative from the 0 point.
Note that if cables are crossed, some steppers work with crossed cables (where order of certain pairs is reversed) - while other steppers do not. This indicates that the internal wiring of the steppers differs between steppers.

Homing

X and Y home well
Z moves down and stops. Huh? Never seen this before. Z stop triggered without z probe connected?

< Reporting endstop status < x_min: open < y_max: open < z_min: TRIGGERED

Issue - Z probe - I have LJ18A3-8-Z/BY-5V. Is BX recommended? What is the difference? [1]. See Instructables article.
Switching the power pins does not allow probe to trigger. Green is the outermost connection - that is assumed signal, middle is ground, red is power. I reversed ground and power
In configuration.h, I set #define Z_MIN_PROBE_ENDSTOP_INVERTING from false to true. No change in behavior - it is normally closed, not normally open
Trying #define Z_MIN_ENDSTOP_INVERTING true - changing it to false. It worked.
I left Z_MIN_PROBE_ENDSTOP_INVERTING at falso - so I changed only 1 thing.

Print Cooling Fan

Cooling fan - when placed close to the stepper motor - does not work! It slows down and stops. Some electromagnetic interference must be happening. Exactly how is not clear. Metal rods of axis appear to have something to do with it.