Lenition happens for several reasons but the two most common in the course are:
1) using the vocative case, which you aren't doing because you aren't calling someone "red" (like how caraid goes to "a charaid" when you're calling someone "friend")
2) if you're combining it with a singular feminine noun, like "oidhche" - so instead of "oidhche math" you use "oidhche mhath" for "good night". The important part here is that you're saying "good night", you're not saying "a night is good". Since you're combining it with night in "good night", there is lenition. If you were to say "a night is good", "tha oidhche math", there would be no lenition.
In this scenario, you are combining it with a noun ("a red coat"), but "còta" is a masculine noun and singular masculine nouns don't cause lenition.
Does that make sense? (I hope so because I may have half-confused myself ;-))
Yes the cloud is lifting! Thank you! Just one more question...how do you know when it's a feminine or a masculine noun? Or is that a very broad subject for a whole other discussion? In which case I will save you from a very long answer and look elsewhere! Thank you for your time. I really appreciate your help!