'lady','girl' and 'woman' all are 'females', 'female' it is a gender classification to distiniguish the feminine entity from the masculine.
When you say she is a female ,you refer to her sex.
Using the word 'woman' refers both to the gender and the age category.
It defines an adult female being.
'Lady' is used in reference to a 'woman' as well, but out of politeness and as a formal way to address her.
It could also refer to a woman of an upper social class. In the Uk it is still used as part of some official titles.
A 'lady' could be young in age,but usually must have passed her puberty phase.
In general it is more of an old fashioned title, that is not used much in dailly speech nowadays.
'Girl' is a female child.
Sometimes the word is used to refer to adult females and could be offensive, if used as a derogatory remark by some men, bearing in mind that the word is used also in the sense of a young woman working as a servant.