Curious, I googled this, the answer is:

Its complementary colors depend on which lavender you are using. Every variation looks crisp and bright with white. The brighter, purple versions looks great with lime green and orange. The grayer lavenders look great with beige, magenta and yellows (gold and warm browns).

If I may add, it also looks good with pink. If I’m not mistaken, I believe I owned a pair of lavender pants when I was a wee lad in the early 70s, and I paired it with a pink-patterned shirt. (To be more honest, my mother did, a woman of fine taste.)

Bonus: lots of pictures. I like this woman’s style. As she says, “Lavender cabinetry is both homey and modern.” Surprised, I would have to agree.