Try to apply the same permissions to your image directory as you did with the app/logs
and app/cache
folders.
You should then be able to clear the cache without any errors.
I haven't used the LiipImagineBundle yet, but i think it's best to clear the cache after each change to the dimensions, otherwise the bundle would have to check if the image was changed on each request (which defeats the purpose of caching)!
Hope this helps.