It doesn't destroy lipid membranes as much as it interferes with their geometry.

The "head" of the soap often has a negative charge (i.e., it is a salt). The "tail" is usually just a straight carbon chain.

The head's charge likes to associate with water molecules as water is polar (the O is slightly negative, H is slightly positive). It's a opposite (partial) charges attract situation. This is the hydrophilic end.

The tail is generally a straight carbon chain, causing it to be non-polarized. It's symmetry and flexibility both help prevent any terminate dipoles from forming. This is the hydrophobic end (although it is less that it doesn't like water and more that water would rather be with other polar molecules). Hydrophobic molecules are effectively trapped together as water excludes them.

Lipids that make up bilayers (like viral capsules and cell membrane). Aside from cholesterol, membrane lipids are similar to detergents in their hydrophilic head, hydrophobic tail geometry but are more complicated as they have 1, 2, 3 tails and 0-1 heads. The types/combos of head and tails that make up a lipid and the mix of different lipids dictates the geometry and physical properties of a viral/cell membrane (proteins also play a key role in shaping membranes).

Detergents wiggle their way next to membrane lipids and disrupt their packing. Rather than forming flat membranes, they create highly curved capsules called "micelles." Some membrane lipids get caught up in that and are subsequently washed away. The cell and enveloped viruses can't function without their membranes, so they die.

The lipids are still there intact (maybe oxidized), just mixed up by the detergent.