Roosevelt was married twice, and his first wife, Alice Hathaway Lee, died in 1884, so it's not her. But his second wife, Edith Carow, died in 1948, at age 87. So unless Lorant interviewed her posthumously, via seance, it can't be her, either.
Our best hope of rescuing this anecdote is to assume that Lorant's research happened earlier (1940s?) while Edith Carow Roosevelt was still alive. But she would have been just three years old at the time of Lincoln's funeral, and while her family and the Roosevelt's family socialized together, even her quoted reminiscence is less than definitive about whether that's actually TR.
Possible? Sure. Probable? Maybe. 100% verified? No way.
From what's presented to us, this sounds like a cool legend
https://www.snopes.com/fact-check/roosevelt-lincoln-funeral/
While she might not have direct memory of the event, it would not be unheard of for older relatives to explain the picture to her when she was older. Just because she doesn't remember it directly does not automatically make the story of the picture untrue.
In the linked article Lorent does not specify when exactly he interviewed Edith Carrow Roosevelt, but I think it is fair to assume that the reference to "in the 1950s" is an assumption made by the author of the blog based on when the article was published, and does not cast any doubt on the timeline.
[0] https://web.archive.org/web/20060507100625/http://www.americ...
https://web.archive.org/web/20090107061334/http://www.americ...
Apparently she was 4 at the time and lived next door:
triceratops•1h ago