When writing internal thoughts within a larger body of text, is it more correct to write it like
... 'She's totally lying.' ...
... She's totally lying....
Commonly, thoughts are set in italics.
A few years ago I asked myself the same question. To answer it, I went through all the books in my library (a few hundred). With few exceptions, in all of them the thoughts were set in italics. In the rest, thoughts were not marked up at all (i.e. neither italics nor quotation marks). I do not own a single book in which thoughts are surrounded by quotation marks.
The MLA Style Blog says you can use both, italics or quotation marks, but points out: "Using italics has the advantage of distinguishing thoughts from speech."
For example, compare:
"Julie! Where are you?" Sarah wailed. 'Why are you never here, when I need you?'
"Julie! Where are you?" Sarah wailed. Why are you never here, when I need you?
If the narration is mostly thoughts, e.g. in stream of consciousness narration, no markup is used. Here is the opening of Virginia Woolf's Mrs. Dalloway, for example:
Mrs. Dalloway said she would buy the flowers herself.
For Lucy had her work cut out for her. The doors would be taken off their hinges; Rumpelmayer’s men were coming. And then, thought Clarissa Dalloway, what a morning—fresh as if issued to children on a beach.
What a lark! What a plunge! For so it had always seemed to her, when, with a little squeak of the hinges, which she could hear now, she had burst open the French windows and plunged at Bourton into the open air. How fresh, how calm, stiller than this of course, the air was in the early morning; like the flap of a wave; the kiss of a wave; chill and sharp and yet (for a girl of eighteen as she then was) solemn, feeling as she did, standing there at the open window, that something awful was about to happen; looking at the flowers, at the trees with the smoke winding off them and the rooks rising, falling; standing and looking until Peter Walsh said, “Musing among the vegetables?”—was that it?—“I prefer men to cauliflowers”—was that it? He must have said it at breakfast one morning when she had gone out on to the terrace—Peter Walsh. He would be back from India one of these days, June or July, she forgot which, for his letters were awfully dull; it was his sayings one remembered; his eyes, his pocketknife, his smile, his grumpiness and, when millions of things had utterly vanished—how strange it was!—a few sayings like this about cabbages.