Squall's Crisis Level is the determining factor. Give him 10% HP and Aura status to increase his Crisis Level to a nice high level. You can also increase Crisis Level by having negative status effects and KO'd allies, but that's not necessary. Doing so will increase the number of hits in Renzokuken.

Crisis Level also increases the chance of a finishing move being used, but does not affect which finisher will be used. The % for those are fixed.

Access to Rough Divide: RD = 100%
Access to Fated Circle: RD = 25%, FC = 75%
Access to Blasting Zone: RD = 25%, FC = 25%, BZ = 50%
Access to Lionheart: RD = 25%, FC = 25%, BZ = 25%, Lionheart = 25%

The Luck stat and getting a perfect Renzokuken play no part in getting Lionheart.