As far as Lebanon, there is no mainstream support whatsoever to settle north of the Blue Line. The article you linked describes the idea as "far-right". I would invite you to talk to an Israeli and ask them what they think about Israel annexing Lebanon.
Gaza is entirely different. There was a centuries-old Jewish presence in Gaza until 1929, when the Jews were ethnically cleansed by an Arab pogrom. That same Jewish-owned land was resettled again in 1946, but the Egyptians ethnically cleansed Gaza again in 1948, and kept Gaza Judenrein until 1967. Israel decided to pull all Jews out of Gaza again in a bid for peace in 2005, but of course we all know how that turned out.