The "serious first season" was really just the first half dozen episodes or so, which was basically the original pilot, expanded with new scenes. That's the real reason that Smith stayed with the ship while the family went South-- he wasn't in the original pilot.
As Christopher points out below, the immediate following episodes are serious and diverting shows, for vastly different reasons. Additionally, there are about 8-10 other episodes that I think are worthwhile within reasonable bounds or more. They can be highlighted for how they reinforce the importance of family bonds, make plain the depths of Smith's perfidy, point out in a non-hysterical manner the impact of an alien race's close contact with the Robinson's and its aftermath, are pretty funny (will eviscerating Smith), or just plain eerie or weird.
These include Invaders from the Fifth Dimension, The Sky is Falling, Wish Upon a Star, Attack of the Monster Plants, Return from Outer Space, All That Glitters, A Change of Space, and even the finale, Follow the Leader. We also get to see Michael Rennie, regardless of the story and effects, in a 2-parter yet, The Keeper. Last but not least, an episode that has been critically pointed to for its psychs-sexual undertones and dark subtext, The Magic Mirror, with Michael J. Pollard.
One can certainly make the case that parts of the first season represented clear turns to the garish silliness that pervaded the second season, But I think that interspersed were productions that could quite reasonably be taken at face value while remaining within the spirit of the original framework of the show without going too far out on a limb..