What do you call a lady being proposed to by a man

The man in this case is the Proposer:

Someone who proposes

and the woman is the Proposee:

1.The person to whom a proposal of marriage is made

^{Definitions from wiktionary}

I wouldn't say they were common words, but it's fairly obvious given context what they mean. As commented by @Mitch: they "sound overly formal or even legalistic". Also note that "proposer" doesn't just mean someone who proposes marriage; it is possibly more common in meaning "someone who proposes an idea".

A man who proposes to a woman is commonly called a suitor, though this term may possibly be outdated in modern usage in favor of similar-meaning words like 'beau' which can, but need not necessarily, connote a proposal of marriage as implicit: see synonyms in the 'beau' link.

Suitor [noun] a man who courts or woos a woman (some dictionaries also say: with a view to marriage., which is the traditional meaning.)

https://en.oxforddictionaries.com/definition/suitor

http://www.dictionary.com/browse/suitor

Example (mine) She is still considering the proposal of her long-time suitor? OMG it's been 8 years now...

A related question has been asked here in 2012: What's the female equivalent of "suitor"? However it is about a woman who proposes to a man, which is very different from what you are asking.

There may not be a common word for the woman being proposed to, in your question, but a less common word 'proposee' has indeed been suggested by AndyT in the earlier answer.

The lady being proposed to by a man is the man's love interest.

Wiktionary:

Noun
love interest (plural love interests)

One who is of interest as a potential partner in love