Don't worry about what the sentence means, just take from it the two verbs it's teaching you, mentir and encher.
That is supposed to be referring to politicians (just a guess). They lie to people/citizens while, at the same time, they fill their pockets with money due to high taxes!!
Yes this one is very common to the lips of brasileiros complaining about their politicians.
I can see myself entering a bar anywhere in the world just saying that and there'd be someone to empathize :D
What is the difference between 'your' and 'their'? How do you distinguish the two?
If you use "seu, seus, sua, suas" it becomes ambiguous.
But if you use deles(masc) and delas(fem) to mean "their" it is not ambiguois anymore