Yes! I think after Water FastLiver-Flush is real good. parasite cleaning before Liver-Flush is also required but for emergency purpose it's better to do the Liver-Flush first and deal with the parasite later.
Make sure to put a dose of some sort of parasite herb/tincture in the oil and citrus potion to take care of parasite coming out because of the flush.
As for your concern about the LF before the parasite cleansing is rightly so as the LF will be more difficult but doable.
By the way vorius, if it's possible please update us on your upcoming LF.