That works, summoning the discarded monster. However, this only works if there is another legal target available. For example, if I use Lumina Lightsworn Summoner's effect when I just have a Mystical Space Typhoon in my Graveyard, that means there is nothing I could summon. and knowing that, I cannot activate her effect. It's like activating Dark Hole when there are no monsters, or Dust Tornado if it's the only Spell/Trap card on the field. Now if there were to be, say, a Ryko Lightsworn Hunter in my Grave already, and I would have a Lumina, then I could discard Wulf Lightsworn Beast, and then target that same Wulf. Since I discard as a cost, THEN I target one.
Same ruling applies to likewise monsters, such as Zombie Master.