No, you can't; that's why it helps - you can use the Site-Discard or Deck-Discard Lost Souls more than once or move a Lost Soul from one site to another, which could be useful for a number of situations, like if you put a Lost Soul in a site before you realized that your opponent uses that brigade, or if you had the Site Doubler in a site alone before you drew; it's actually pretty useful for site decks and stuff.
