ThreeLac is just a potent anti-yeast probiotic. It should match well with your intestinal cleansing formulas, particularly if you have a yeast problem. The only concern I'd have here would be related to too strong a die-off reaction at the same time that your body is trying to coope with the toxins being moved around with the intestinal cleansing formulas. If you discover that taking ThreeLac with the ICF's is too much to handle, delay it for a bit, or wait until you've completed the ICF's.
It shouldn't interfere with other cleanses at all, although you probably don't want to take any on days when you're drinking Epsom Salt or salt water, since you'll mostly just flush out whatever ThreeLac you've taken.