This is from the PDF I have:
BATTLE LANCE:
"The Battle Lance formation receives the equivalent of a 6-point Lucky Special Pilot Ability (see p. 54), except that it is useable by any unit in the Battle Lance, rather than limited to any single unit. This formation ability need not be assigned to specific units, and may thus be called upon after a failed attack or Control roll desired (to a maximum of 6 times for the entire formation). As with the normal Lucky SPA, only one reroll per failed attack or Control roll is possible."
SUPPORT LANCE
"Before the start of play, each Support Lance must designate one other formation type in its army to support. For every 2 units in the supported formation that make use of a formation-provided bonus ability, 1 unit in its Support Lance receives the same ability. This bonus ability is retained as long as the Support Lance still has three or more active units on the field; they are not lost if the supported lance is reduced below its own ability to retain the bonus ability. If the Support Lance is supporting a Command Lance, it receives the two SPAs assigned to the Command Lance’s noncommander units, assigning one SPA each to any appropriate Support Lance unit. However, the Support Lance does not receive the commander’s Tactical Genius Special Pilot Ability."
With that in mind, Im thinking the Support Lance also gets at least 2 Luck points. Because all 4 units are able to draw upon the SPA of the Battle Lance. But they might also get the whole 6 points. It would be odd for them to recieve nothing...if that was the case, youd be better off chosing another formation type to support.
But I too would like to know the answer to this question...