Can "lad" only be used to address a male, while "mate" both male and female?
Lad is another name for a boy or a young man.
I suspect that lad is becoming increasingly rare to hear, I might be wrong, but I think this word still resists in the north of England, especially in Yorkshire. The female equivalent of lad is lassie or lass.
Lad is often used as an affectionate term as in
He's a good lad, his heart's in the right place.
Whereas mate is an informal word meaning friend, and can be used for both men and women. The following expressions are clichéd but will give you an idea of how the word is used in conversation:
I'm going down the pub with me mates (more likely said by a man.)
Me and my mates had a great time down at the local (could be said by either a man or woman.)
She's my best mate, I love her to bits
Used in the traditional macho form of 'On Fridays I go to the pub with me mates/the lads/the boys', I feel sure there were at one time regional variations. 'Lad' is still associated with the north of England and Scotland, an accompaniment of 'lass' or 'lassie'. (My wife was delighted many years ago in Edinburgh, when an older gentleman, of whom she had asked directions, called her 'lassie')
Professor of Socio-Linguistics, Peter Trudgill, in his work on the the Norfolk Dialect, and in stressing the sudden cut-off of Norfolk, in the area close to The Wash, has put a marker on the village of Terrington St Clement. In a Terrington pub, Trudgill argues, they will be speaking the Norfolk dialect and the young men will be called 'boys' (pronounced 'buuys'.) About 7 miles down the road and across the Great Ouse in Sutton Bridge, the pub company will be speaking a distinctively northern dialect and the young men will be called 'lads'.
That is not to say that 'lad' is not used in the south of England, in context. 'He's a good lad'.
'Mate' I feel sure originated, in this sense, in Cockney English, though it has a long and complex history, and is now heard far and wide. It is also extensively used in compounds, such as 'flat-mate', 'dining-mate', 'drinking-mate' etc
It should be borne in mind that there are many other meanings to these words. Calling someone a 'lad' can be in the sense of a boisterously macho young man 'Tony was a bit of a lad for the women' (ODE).
'Mate' has many meanings, including as a rank in the Merchant Navy, as an officer subordinate to the Master, e.g. A First Mate. It is also used occupationally such as in 'plumber's mate'
This is potentially a vast subject.