John Lightfoot on Luke 18:13

[And the publican, standing afar off, &c.] I. That the Israelites, when they went into the Temple to put up their own private prayers, went beyond the outward court, or the Court of the Gentiles, into the Court of the Women; this, amongst other things, makes it evident, viz., that in that court were placed thirteen eleemosynary chests, into which they threw in their voluntary oblations: which was done by the widow with her two mites in that place.

II. It is a question whether any person for his private praying might come as far as the gate of Nicanor, or the Court of Israel; much less into the Court of the Priests, unless the priests only. We read of our Saviour's being in the Court of the Gentiles, viz., in Solomon's Porch, and that he was in the treasury, or the Court of the Women; but you will hardly find him at any time in the Court of Israel. And the negative upon their entrance into that court is confirmed, at least if that rule avail any thing which we meet with in Hieros. Beracoth: "R. Joshua Ben Levi saith, 'He that stands to pray, it is necessary that he first sit down, because it is said, Blessed are they that "sit" in thy house.'" Now it was lawful for no person to sit down in that court but the king only.

III. That therefore this publican stood so much further off while he prayed than the Pharisee, was probably more from his humility than any necessity that lay upon him so to do. For though the heathen and publican go together in those words of our Saviour, "Let him be unto thee as a heathen man and a publican," yet it is a question whether the publicans, if they were Jews, were bounded to the outward court only, as the heathens were.

[He would not lift so much as his eyes unto heaven.] What needed this to have been added, when this was the very rule of praying, "Let him that prayeth cover his head and look downward." "The disciple of the wise men, when he stands praying, let him look downward." But were those of the laity or of the common people to do thus? If not, our question is answered, that this man (otherwise than the vulgar was wont) in deep humility and a conscience of his own vileness, would not lift up his eyes. But if this was the usage of all in common, that whilst they were actually praying they must look downward; yet probably in the time that they were composing themselves to prayer, they might be a little lifting up their eyes towards heaven. "If they pray in the Temple, they turn their faces towards the holy of holies; if elsewhere, then towards Jerusalem." And it would be a strange thing if they were not to have their eyes towards heaven at all: indeed, when they began to pray, then they looked downward.

[For more info, please see A Discourse upon the Pharisee and Publican by John Bunyan (341k).]