"... Is the outcome different if you do it different? As someone else already explained to me that adding in lye creates sodium citrate, which apparently is not the same thing this would be to increase bubbles, right?..."
The outcome is not any different whether you add the citric acid to the lye water or if you add it at trace. There is still plenty of free lye available at trace. The lye converts the citric acid to sodium citrate. That reduces the lye available for actual saponification, if you haven't compensated by adding the appropriate amount of extra lye.
Sodium citrate doesn't add bubbles/lather. What it does is react with hard water ions to keep those ions from reacting with your soap and turning it into sticky soap scum. More soap = More bubbles. Less soap scum = Less grey buildup on fabric, tub, and skin.
"...What you don't use citric acid for is lowering the PH. If you lower the PH too much, you won't have soap anymore, just a globby mess. Many people mistakenly think you can make soap with a lower PH so they add some kind of acid to their soap and all the really do is neutralize some of the lye, effectively increasing the SF. ..."
What Obsidian said ^^^. I couldn't say it any more clearly than this. If a cleanser with a low pH is a big deal, then lye soap is not the answer -- synthetic detergents are the direction to go. Also, people seem to want soap to do many things well -- be a conditioner, cleanser, whatever -- all in one go. It doesn't work that way.