Found some info for you....but I took a quick peek at your tree first, and it seems to me by what you have on there that you suspect Henry didn't really die in AR after all, and I don't think so either.
A great grandson of Henry Lamey didn't think so, and posted a query in the Indianapolis Star paper, dated Sep 2, 1987 in the Indiana Ancestors section (attached).
So yeah, the info you have attached to your tree on Henry Lamey that died in 1951 in Indiana MAY very well be the same Henry that drifted into AR after the 1900 IN Census, married Lula in 1903, fathered 2 children, then abandoned them all and went back to IN by 1910 as if nothing ever happened.....
Yes, Lula is listed as 'widow' in that 1910 AR Census, but back then, not the first time a woman has declared herself a widow when she wasn't; my own great grandmother did the same thing - she was not widowed early on; great grandpa stormed out and moved to another part of the state. She started declaring herself a widow in City Directories the year he walked out, and continued to do so until he really did die over 12 years later. [They were Catholics and never divorced] Some women did this because of the stigma/shame attached to being a divorced woman back then. :-0
Also on that 1910 AR Census where Lula Lamey states she's a widow, you notice by where the 2 kids [Harlman & Cora (Opal)] are listed, it states they were born in AR, their father in Indiana, their mother in AR. Uh-huh. Another reason to suspect that that's the same Henry Lamey.
So, did these two [Henry & Lula] officially divorce? No telling without a divorce record. If they didn't, they're both bigamists. [One or two of my ancestors were bigamists also. Quick, cheap, and easy to declare yourself widowed and move on when your spouse is in the wind in another state, and/or just pretend it all never happened to begin with.]
When Lula remarries Jim Carroll in 1912, she's using her maiden name - Miss Lula Bryant:https://www.familysearch.org/ark:/61903/3:1:S3HY-67Q7-8XH?i=...
I notice you don't have the 1930 Census for Jim and Lulu Carroll attached, here it is:https://www.familysearch.org/ark:/61903/3:1:33S7-9R4B-3ND?i=...
I found the 1951 obit for the Henry Lamey that died in IN (attached); no mention of a first wife or those 2 kids. Princeton Daily Clarion, Aug 19, 1951.
His father Andrew Lamey's 1928 obit. Evansville Press, July 12, 1928.
His mother Christina's OH death cert attached.
His brother William's 1948 OH death cert: https://www.familysearch.org/ark:/61903/3:1:S3HT-DYF9-XSW?i=...
His sister Margaret's obit - Princeton Daily Clarion, July 13, 1942.
Notice in Princeton Daily Clarion, Feb 16, 1914 that Henry's mother died in Cincinnati.
Henry's sister Anna Marie's 1946 obit, Evansville Press, Feb 20, 1946.
Anyway, good possibility that's the same Henry.