According to the Oxford English Dictionary, milady emerged in 1778 that partially came from French:
Partly < French milady , title used when addressing or speaking of an English lady of high rank (1727 in Voltaire; 1754 as milédi ) < English my lady (see lady n. 3a), and partly representing a colloquial pronunciation of my lady (see above). Compare Italian miledi (18th cent.; < French).
This first definition was:
Originally, representing the usage of foreign (esp. French) speakers: a form of address to or title for an English (occas. French) noblewoman or an Englishwoman of wealth and influence, usually substituted for the person's name.
This was gradually adopted by the English, so it was not solely a contraction of "my lady". Similarly, milord came from French as well:
< French milord (1610 or earlier in form milord ; 1552 in Middle French in form milourt with reference to an English nobleman (Rabelais); c1480 in form millourt with sense ‘nobleman, rich man’; also in form milor (1634 or earlier)) < English my lord (see lord n. 15; compare milord , milorde as occas. spellings of my lord in early modern English).