The short answer is yes, fatty acids from a guava could hypothetically be used to fuel a butane lighter. I don't personally know of any instances of this being performed, and online research yielded no results - based on my knowledge of this process, there are probably other biofuels better suited for hydrocarbon extraction (since guava have such little fat content), and other end-products that guava are better suited for (possibly alcohol fermentation due to high amounts of sugar in fruits). However the fundamental chemistry remains the same, and given the right tools it should be possible.
It should be noted that gasoline and butane are not the same thing; butane is a specific hydrocarbon with the chemical formula C4H10, whereas gasoline is a mix of several hydrocarbons including butane and several others. Butane is also frequently used in gaseous form. Depending upon the construction of the lighter, it may not be possible to fuel a butane lighter with gasoline, or vice versa.
However, both butane and gasoline are based on hydrocarbons, and fatty acids are essentially hydrocarbon chains with a carboxylic acid molecule at one end. Removing the carboxylic acid should render the hydrocarbons free to be used for other purposes. Unfortunately the nutritional information provided in the photo doesn't tell us enough about the chemical structure of the fatty acids, so we can't really tell what hydrocarbons they could form. The only exception is the Omega-6 and -3 fatty acids, although these names only describe one portion of the hydrocarbon, and neither of them are de facto progenitors of butane.