This trinitarian 'proof'-text seems too ridiculous to even bother with, but some trinitarians appear to be serious about it. It goes this way: when we read Gen. 19:24, we find there are two different persons who have the only personal name of God, "Jehovah," (or "LORD" in some mistranslations). Therefore these two different persons with God's personal name show the "plural personality" of that one God.
Even if we assume this to be a correct translation, it seems obvious that it can be honestly interpreted as a simple repetition of the same person's name. That is, the very same person who produced the brimstone and fire, Jehovah, is also the one who rained it down upon these cities.
The explanatory note by trinitarian Dr. Young in Young's Concise Critical Bible Commentary, Baker Book House, for this verse states: "JEHOVAH...JEHOVAH, i.e. from Himself."
If that is the correct explanation, then this scripture might provide a somewhat parallel example: "And King Solomon gave to the Queen of Sheba all that she desired, whatever she asked besides what was given her by the bounty of King Solomon." - 1 Kings 10:13, RSV. (Cf. KJV.) Even though this is a very literal translation of the original manuscripts and the one personal name of King Solomon is actually used twice, we surely don't believe there were two different persons making up the one King Solomon! Wouldn't we interpret this as Dr. Young (and others) have done with "Jehovah" above? That is obviously how the Living Bible, NIV, MLB, NASB, etc. have interpreted it. ("King Solomon gave her everything she asked him for, besides the presents he had already planned." - LB.)
Another honest explanation for Gen. 19:24 given by trinitarian scholars themselves is that the use of the phrase in question ("from the LORD out of heaven") is in doubt. The very trinitarian New American Bible, 1970 ed. (Catholic) encloses the last part of Gen. 19:24 in brackets: "the LORD rained down sulphurous fire upon Sodom and Gomorrah [from the LORD out of heaven]." And the preface to the NAB tells us: "Doubtful readings ... appear within brackets." - p. 45, St. Joseph Edition.
That is why these trinitarian Bible translations have actually omitted that doubtful portion: NEB, REB, AT, Mo, LB, and GNB. (E.g. "then the LORD rained down fire and brimstone from the skies on Sodom and Gomorrah." - New English Bible.) And others, like the NJB, have rendered it "[Jehovah] rained down on Sodom and Gomorrah brimstone and fire of his own sending." Certainly no trinitarian Bible translation would do this if it could possibly be used as honest trinitarian evidence!