You can't produce two mana just by doing as you state. This is because tapping as part of paying the cost of an ability doesn't pay the cost of another spell or ability (C.R. 117.10). You would need to tap a creature you control other than Lifespring Druid as part of activating Springleaf Drum's ability if you want to use Lifespring Druid's mana ability.
Springleaf Drum + Lifespring Druid?