I have seen it, and so have many others.
One doesn't have to come out and say "I saved myself" for it to apply. It's how ones theology reflects these things, not in coming right out in making the statement word for word. So, we go by what their theology says.
For instance, those in Matthew 7:21-22 claiming their works, would have never stated "I am saving myself" but their theology shows differently. They were exercising a works based religion, not a relationship with Christ. As a matter of fact, it would be accurate to say these types did claim Christ, yet they trusted in themselves and their works, yet remained in their sins, because their sins were still being imputed on them; Matthew 7:23.
One can express belief in "unconditional election" in their teachings having never heard the term used in an acrostic or otherwise. The same can be said for other points of TULIP.
One can also believe in "Limited Depravity" from "LILAC" without knowing the term, yet they reflect it in their teachings. The same applies for the balance of "LILAC."
One who rejects the truth of OSAS may not know the term, but believe they will or can lose their salvation. This presents several problems theologically. One, they aren't truly trusting Christ alone, though they would argue they are, and secondly, no matter how much theological acumen they possess, they still have a works based religion. Thus the term "Carnal Security" would apply to them.
Another consideration is "I elect Christ." There are many who place their faith in a prayer said, or in "they chose Christ." This is not accurate, it is God who chose and God who saves alone. The Scriptures teach dogmatically He calls, elects (chooses). Yet I see many people point to a prayer they said when asked about their salvation. Therefore "I Elect God" applies to them. By the way, there are those within the church who need to be evangelized as well as those without.
Thus, one doesn't need to come out and make a statement such as "Limited Depravity" or "Carnal Security" for these to be their true beliefs when such beliefs are reflected within their theology (teachings). So, one can say "I trust Christ alone, period!" from here to eternity, but the real truth comes out in their teachings and leanings theologically.
Lastly, I have addressed each and every one of your points, yet you fail to show me even
one point of LILAC that isn't reflective of non-Calvinist theology with proof they don't teach this, or even a mere rebuttal of any point! Perhaps you cannot rebutt them?
You've also alluded that no non-Calvinist believes any of the points. This is blatantly false, as the LILAC accurately represents the theologies within these camps. I've demonstrated above how this is true and exactly how it applies.
Here is a link that expresses this in more detail. Should I expect a copout excuse that the link isn't "pure Bible?" If that is your point, then please lose the Spurgeon quote on your signature under the same principle.
Here it is:
http://www.prca.org/standard_bearer/volume74/1997oct15.html#Lilac
- Peace