The thing is that the name
Lavender doesn't have a nickname. Well you could call her
Leni as someone suggested but
Leni isn't really a nickname for
Lavender. It seems kind of weird naming a child
Lavender and calling her
Leni, it's like naming her
Hyacinth and calling her
Sue, it just doesn't make sense.
The only nicknames you get from
Lavender are
Lala and
Wendy (but even those don't really make sense). If you are really trying so hard to find a nickname I'd wonder if you really like the name
Lavender or if you prefer another name.