How about a medium tan (shade value slightly darker than the lavender)? Then the other colors suggested could be used for accents. The carpet would have to have some "life" to it so as not to "dull down" the room. Have fun!
I agree with green/blue grey - or if there's not a lot of pattern in the room a neutral grey/heather carpet with throw rugs - or a patterned rug with white/lavendar (like some Indian rugs...)...Please don't try to match the lavendar exactly in the carpet- or use purple - it won't work...
What other colors do you have in the room? I had a room that had lavender walls and I used my bedspread to find a color for the carpet. I even took the bedspread right to the carpet store! I picked out a sage green carpet and it looked wonderful, very cottage/country.
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