The first time Max goes to Lilly's she is wearing a strapless top with horizontal pinstripe. When she wakes up, though, her top has shoulder straps and no stripes.
Lily makes a big show of wiping all Max's fingerprints from Walter's home, calling Max an 'amateur' for never having done it before, but opens and closes the front door with her bare hand when she leaves. This means Max could not be placed at the scene but Lily (the expert) could.