A more advanced lace pattern may have action on both right-side and wrong-side rows. Or it may have rows with non-balanced yarn-overs. Or it may have both. The decreases that balance the yarn-overs do not have to be on the same row with their yarn-overs. Many beautiful lace patterns with rippling or scalloped edges are created using this method. But, these patterns can be trickier to work because the stitch count changes from row to row, even when the fabric is not intentionally being shaped. And this type of non-balanced patterning can even be a slick trick — the Hemlock Ring shawl/blanket is an example of a lace where a non-balanced pattern stitch causes the fabric to grow circularly.
Decreases also have direction. And those directions matter. A decrease leaning towards a yarn-over can make the hole smaller, diminishing the lace effect. Decreases lined up can make knit wales move around a fabric, making little outlines or adding details such as stem lines to leaf-shaped lace patterns. The two basic decreases are right-leaning and left-leaning. A regular right-leaning decrease is k2tog. A regular left-leaning decrease is ssk. Both turn two stitches into one.
When working reversible lace, these basic directional decreases now involve four stitches rather than two, because you are decreasing two stitches on each side of the work. One decrease is worked knitwise and the other is worked purlwise. These are essentially the same decreases used in double-knitting. For a right-leaning decrease, you'll need to rearrange two stitches, then work k2tog and ssp.
For a left-leaning decrease, you'll still need to rearrange two stitches. But this time, you'll work ssk and p2tog.
If you are working standard Western knitting, then the right-leaning reversible decrease involves changing the stitch facings of both purl stitches and the left-leaning reversible decrease involves changing the stitch facings of both knit stitches. However, if you are working combination knitting, then all the knits face right (east) and all the purls face left (west). For combination knitters, you will need change the stitch facings of all four stitches when working a right-leaning reversible decrease, but you won't have to change the facings of any stitches when working a left-leaning reversible decrease.
I haven't yet experimented with 3-into-1 decreases, but they should be similar. You'll need to rearrange six stitches from 6-5-4-3-2-1 into 6-4-2 and 5-3-1, and then work both a knit-side and a purl-side decrease.