Do the best you can to find organic but if you can't you can't.
"Breaking out" on a cleanse is not necesarily a bad thing cause it just means that some detoxing is taking place, unless what you're having is an allergic reaction.
I don't know enough of the chemical difference between lemons and limes to know how much difference there is so I wonder if your reaction to the lemons was just a cleansing reaction. Just from first impressions it's hard for me to think that there is that much difference bewtween lemons and limes that one would be allergic to one and not the other.
BTW I have the "original text by Stanley Burroughs" in a PDF file and I did a search for this Espen fellow you mention and there's no mention of him. Where did you read this thing about mixing it with juices?