The same thing that happens when normal Witch's consume Lobelia pills the Lobelia was used in a Episode in TO called Gonna Set Your Flag On Fire when Cassie told Rebekah that the "patients" in the Dowager Fauline Asylum are given capsules containing Lobelia flowers, which makes it impossible to concentrate and thus decreases a Witch's ability to perform magic, as it requires concentration in order to produce effects.
In herbalism, Lobelia has a long history of use by various peoples as a nervine, anti-asthmatic, emetic, and as a tobacco substitute (In fact, it actually works on nicotine receptors as a nicotine antagonist, although it contains no nicotine). Both Native Americans and practitioners of folk medicine recommended it be smoked for asthma, and it decreases nicotine cravings. Lobelia falls under the influence of the planet Neptune and is often used in witchcraft for love spells.
In short, It just makes Witches unable to concentrate and when a Witch can't concentrate they can't use any spells so the effects would still work on Witch-Vampire hybrids.