Nope; as noted, "I haven't run across anyone in my personal life...", so this would fall under the "anecdote" category. :)
I want to see a proper double blind study done of this.
I look at an LCD all day, then sometimes some more at home. I do not suffer from any eyestrain I can detect.
Similar to the anecdote/data duality is the fact that not everyone is affected by things the same way. You may be one of the lucky few or lucky many who aren't negatively impacted by looking at an LCD all day. I know that my nearsightedness is markedly worse at the end of any workweek where I've been staring at the monitor all the time, and that my eyesight is noticeably improved after spending several days not staring at something only a couple feet away. YMMV, and all that.
The impact of backlit screens on circadian rhythms has been studied, if memory serves. Some quick googling pulls up a goodly number of hits, including a couple actual studies just in the first page of hits. Changing from regular web-wide Google to Google Scholar produces more hits for studies.
And more specific to eye strain are these hits. I haven't waded through, but the number of hits (524) and the titles of the first page of hits suggests that this is an area of study. This one in particular sounds like what you might be looking for: Comparison of eye fatigue among readings on conventional book and two typical electronic books equipped with electrophoretic display and LC display . This link to the paper is paywalled, unfortunately, but you might be able to ferret out an open copy of it somewhere.