The use of dish detergent sounds good but it is not recommended by the major manufacturers. That might have changed since SA and Rio said that years ago, I haven't nor do I have a reason to look lately.
Ivory bar soap is just that, soap and has no detergent in it. The manufacturers said detergent could leach the plasticizors and hurt those expensive lines.
In the short time I tried detergent I found it did indeed clean the line but it got the lines squeaky clean. That squeak was a sign of friction to me and the line seemed to slow down so much I had to slosh line juice on it to make it usable again. The line dressing left a wet finish that, though real slick seemed to attract dirt and create other problems.
On SA lines with AST as well as newer Wulff and Rio lines I use the the gray 3M pad shown in Silvers post. It takes a microscopic layer of coating off and brings a new, dry surface to the top. Because this surface is slick yet dry it works as needed and lasts quite long because it attracts no dirt.
If a line needs lube or dressing I use Glide or Rio dressing which requires time and elbow grease to put on and do right but when you're done it is slick, sort-of dry and very long lasting.
For a quick speed up the SA bottle of lube really works. It's slippery and wet but so is the water I use it on as when in a boat when salt water fishing.
For real skanky demo and instruction lines that might have been blackened by parking lot oil and grease the Mr. Clean Magic Erasers bring color back to them. No matter which line I have to use that on I lube it with the manufacturers or another line manufacturers line dressing.
To my way of thinking good fly lines cost too much to experiment with using stuff found under a kitchen counter or over the work bench. Real line treatments don't cost too very much and aren't ordinarily water soluble like a famous auot product that will probably be mentioned in this thread.
I typed all of this knowing it was typed several times before on this forum.
If I was out fishing like I should be I wouldn't be sitting inside punching a keyboard.
Boredom is EVIL!