Just not over washing your hair is helpful. I've had pink, lavender, and blonde. I like using dry shampoo and definitely don't wash my hair every day to keep color longer.
Purple shampoo and conditioner like Shimmer Lights helped when I had pink and purple hair, to keep brassy tones away, even though it's mostly for platinum blonde hair. If you do lavender, leaving in purple conditioner will really keep the color looking nice. I actually got my hair from platinum to lavender one time just by leaving in purple conditioner for a long time lol. Not the best way to do it, obviously. Also, purple shampoo can be harsh so don't overuse it.
My friend who has pink hair mixes a small amount of her pink dye into conditioner and uses that - I think I did something similar but don't really remember, maybe look into that?
I'm weird, and whenever I see girls with platinum hair I REALLY like I chase them down and ask them what they use. I've tried a bunch of products, but shimmer lights is still my favorite.
@Barbarella that's a really good tip on the Olaplex.. I also have platinum hair but I recently cut it short because it was damaged (I did a lot of shit to it is why, really). I don't think my stylist uses it, but otherwise, she does a great job with platinum.