Can we find evidence in the Old Testament of Jesus appearing to men? If our Lord spoke to men in the OT (like to Abraham in Genesis 18), why don't we see those words printed in red letters, as some Bibles do to mark Jesus' words in the New Testament?
Though all Christians believe in the eternal existence of Christ (see John 1), there is still debate as to if and when Jesus appeared in the Old Testament. We believe (as do many Bible scholars) that Jesus appears repeated in the OT, often as the Angel of the Lord, including in the scene you mentioned from Genesis 18. Nevertheless, not all scholars agree on which OT scenes contain appearances of Christ or even if such appearances happened at all.
Therefore, Bible editors generally do not apply the red lettering technique in the OT due to the uncertainty over which words belong to Christ. Remember, when a Bible's editors choose to mark Jesus' words using red ink, they are offering an interpretation of the text in the sense that they are deciding for the reader which words were spoken by Christ.
Since this is a matter of judgment, many Bibles use no red lettering at all, and the ones that do highlight Christ's words do so sparingly, usually limiting their use of red lettering to the words Jesus clearly spoke in the New Testament (i.e., the Gospel and Revelation). If editors were to extend their use of red letters to the OT, they would be forced to make increasingly difficult determinations for which words belonged to Christ.
Consequently, do not base your own interpretation of the Bible on how an editor may have chosen to color the text. These techniques may be helpful guides, but they are not divinely inspired nor infallible.