First, Season 1 of Lost In Space:
In episode 9, the protagonists discover that their spaceship can be fueled with "petrified biomass" which has built up over hundreds of years in the cave. If I remember correctly, there was also some 'secret ingredient' that made this specific bat guano from that specific cave have the right minerals or chemicals in it or whatever. Point is, Lost in Space is not really science fiction but rather science fantasy (a fantasy story with a spaceships/future setting).
Secondly, using biomass as fuel for rockets:
When talking about fuel, specific energy is a very important metric. Certain things, such as jet fuel or coal have a high specific energy density that they contain a lot of potential energy per unit mass. That's why these are used in power plants and engines.
Some specific examples from Wikipedia:
- Jet Fuel: 43 MJ/kg
- Coal: 30 MJ/kg
- Dried cow dung: 15 MJ/kg
- Ethanol: 30 MJ/kg
- Biodiesel: 42 MJ/kg
- Glucose: 15 MJ/kg
- Liquid Methane: 55 MJ/kg
- Liquid Hydrogen: ~130 MJ/kg
- Uranium: 80620000 MJ/kg
- Deuterium: 579000000 MJ/kg
As you can see, dried dung doesn't have that much specific energy (comparatively), and this makes sense if you think about it: Creatures eat food to consume energy and excrete that which they can't extract energy from. Evolutionary, a creature which doesn't extract as much energy as possible from it's meal is at a disadvantage.
Unless the "petrified biomass" somehow contained a high amount of radioactive isotopes, there is no fuel which could power the ships as it does in the show. Real spaceships (capable of launching from an Earth-like planet) are usually >90% fuel by volume and mass. In the show, fuel tanks are a small part of the spaceship and the spaceships are clearly able to hover and preform SSTO maneuvers with ease. Something like that requires advanced nuclear technology or clarke-tech (magic).