There are two schools of thought on removal of Lilly of the Valley plants, and both are listed below. You have started the organic path by digging out the plants now, but this method will require the bed to be covered for the 2022 growing season. Applying table salt to the soil will kill the Lilies of the Valley and most other organisms in the soil. The salt may also prevent the growth of plants over the next several years, depending on the salt concentration.

ORGANIC: Digging and removing the roots of this plant is the most effective organic control method, and this is best done when the soil is moist. This may be done most easily by running a flat bladed shovel through the soil below the root level and then sifting through the uprooted mass to remove the entire plant. The plants should then be disposed of properly. Repeated treatments will be needed as it will re-sprout from any root fragments that might remain. Smothering may be the easiest organic method of control for larger monocultures. This can be done in early spring as the plants begin to sprout, or as late as early summer. Be sure to cut mature plants to the ground level before smothering. Lay down a tarp, old carpet, landscaping cloth, cardboard, black plastic, or 8 to 10 layers of damp newspapers over the entire plant bed. Then cover this material with a thick layer of mulch, soil, or gravel, and leave this covering in place for one full growing season. If you use paper or cardboard with mulch for smothering you can later install new plants into this already-prepared planting bed.

CHEMICAL: Application of a glyphosate-based herbicide (RoundUp, etc.) will control lily of the valley, although several applications may be necessary. The best times to spray the plants are early in the spring when the leaves are still tender and while the plants are flowering. Always read herbicide labels carefully before use and always apply according to the instruction on the product label.

I hope this information helps and have a great gardening season.