This is my name. Irish people I've met pronounce it "kayt-lin" (despite that allegedly being the English way!), whereas some Scots and English say "kat-lin". However, I'm Scottish and most Scots do tend to say "kayt-lin", but interestingly there are people from various countries who say "kat-lin". This includes people I've worked with from Syria, Italy, Portugal, India and South America. A lot of French say it more like "kat-eh-leen", which is probably closer to the medieval French "Cateline". There were at least 3 other Caitlins in my year in high school.
I think if you want to pronounce this name "Kate-Lyn", you should spell it "Katelyn" or something similar.Caitlin is not pronounced this way in Ireland - Irish names always have non-intuitive pronunciation to English speakers. Caitlin is no exception - it can be anything from "Catleen" to "Coytleen" to "Coshleen"(?) depending on the area of Ireland. Never "Kate-Lyn" though. I'm not hating on Katelyn though - I actually much prefer this to both the spelling and the Irish pronunciation of Caitlin!