Insecticidal Soaps can be broad spectrum pesticides and can kill whatever it contacts. The advantage is that IS is pretty short term and when dry has no residual affect. Most likely what you saw with the ant "attacking" the Lady Beetle was a dispute over whose food that was rather than an ant "protecting" the lace bug.
Dish soaps are detergents, not soaps in the sense that they are made from petroleum products not by reacting fats with a caustic substance as true soaps are. Detergents can harm plants if not washed off, while soaps need not be, at least in my experience. To make Insecticidal Soap mix 1 teaspoon of a real soap in 1 quart of water and spray. Nothing more needs to be added.

Truly, the most efficient soap for controlling insect pests is commercial insecticidal soap. These products are manufactured especially for the purpose and actually have a LABEL with good directions! ;-)

Are you sure you have lace bugs and not aphids. Aphids have pear-shaped bodies and the many species may be colored different. Lace bugs are small dark insects with clear wings (adults) or without (nymphs). Aphids can be host specific or effect many different hosts. Lacebugs will often be host specific. Aphids are easy to treat. Lacebugs will give you headaches if relying on soaps or oils and the like.

Aphids are typically "herded" by ants, who use the honeydew secreted by the aphids, and in turn provide protection.