We'll set the world on fire

Lucifer's natural form is that of a humanoid. She largely has the same appearance as she does as a human (blonde hair, blue eyes etc), but there are some distinct differences. First, she has two large black wings on her back, resembling those of a bat (non-feathered). They once had feathers when she was still an angel in Heaven, but upon her Fall, the feathers burned away which left telltale scars on her wings, much as her Fallen brothers and sisters suffered as well. Lucifer's eyes also taken on an iridescent, glowing blue color, so much so it looks like her eyes are made of blue fire. She also has a black aura that pulsates off of her as though it was fire radiating from her body.

As she is a shapeshifter, Lucifer can take on other forms. She rather enjoys taking on human form, in which she appears as she does in her icons and the GIFs on this journal. Unless someone is either an angel or a demon, or someone that has such lineage or psychic/aura-reading abilities that allow them to sense the supernatural/demons/angels, they cannot tell she is anything other than human unless she chooses to reveal herself. Lucifer, while being the queen of Hell, can also register as being an angel just as much as a demon because she was born an angel.

Lucifer can take the shape of any animal she pleases as well. Though she far prefers walking Earth in human form. Only if it tickles her fancy or if the situation necessitates it will she take on animal form.