Here are some thoughts regarding the meaning of the title of the book. I’m using the Penguin Classics, Watt’s translation edition.
Boethius faced a sudden and brutal change in his fortunes, and this caused him to “wander away” from himself (p. 16 – c.f., Dante’s awakening in a dark wood). At the beginning of the book, we see what this wandering away from one’s self looks like. The poetic muses are by his side, feeding him sugary poison, ‘dictating words’ to him and seducing him as a group of “sluts” (or “harlots”) may seduce a lonely man (pgs., 4-5). It seems he is actually out of his mind and then he becomes aware of Lady Philosophy standing over him. Her appearance is extraordinary, but one aspect, in particular, is noteworthy here (I will attempt to unpack her appearance more in a different post). “She was so full of years that I could hardly think of her as of my own generation, and yet she possessed a vivid colour and undiminished vigor” (p. 4). I think this is important as it indicates that she isn’t Lady Philosophy in relation to a particular school of philosophy, rather she indicates what is referred to as Perennial Philosophy (though of course Boethius didn’t use or know this term).