Well, the obvious way to tackle pop / rumble is a hefty low cut. On spoken voice, you can usually do away with everything below 120 Hz, sometimes even higher (up to 500 Hz may be suitable in some rooms). Add a shelving filter to take away some of the low mids a bit more gently.
The danger is that you end up with a thin “telephone-like” sound. This is easier avoided if the microphone has a good bass response by itself. Proximity effect does a lot here, as ideally with a large-diaphragm condenser in the near field (with a proper pop screen). Obviously those are not practicable for your application, but most cardoid dynamic mics are also pretty fine and can nicely be scooped out in the EQ without sounding thin.
OTOH... why do you use lavalier mics but placed in a way so the speakers can directly breath into them? That's not the point of a lavalier. They're designed to give a full sound despite indirect placement, which often requires boosting the bass; obviously this exacerbates all the problems with plosives. And the foam guards for those mics are specialised at reducing wind noise, not pop killers.
So if you need close mics for reasons of e.g. feedback, use microphones that are suitable for this placement – either classic hand/boom-held SM58s (or a wireless variant), or headsets.
If you use lavaliers, make sure they're actually placed as lavaliers, i.e. on the speaker's clothing.
Apart from mic placement and EQing one more important thing: Make sure even the nastiest pops don't overdrive the preamps. If that happens, the noise spreads out far higher in the frequency spectrum as it naturally would, so any high-passing afterwards won't work properly.
If all fails, don't despair: there's still a last resort, which is trimming away the pops by dynamic compression. Don't do this unless you have to, but it can be quite effective. Make sure to use fast attack and pretty fast decay – limiters tend to be set up in a suitable way. If you don't have preamp distortion, best only process the low range at all, i.e. a multiband compressor is a good choice. Set the low band to 0-300 Hz, ratio 24:1, threshold so normal loud voice just doesn't cause any gain reduction. If you're fancy, place an additional high-cut of 60 Hz in the side chain, so only
pops will trigger.