Ricë lucë Nauco i haurallo.
Rike luke Nauko i haurallo.
A potential idiomatic expression from the Middle Earth.
If I am understanding the language properly, there is no "k" in Sindarin.
"c" is always hard like in cake.
Thus the phonetic rendering of "ke" in Rike and luke is rendered as "cë."
The only problem with your argument is that this is a Quenya sentence.
There is no "problem" with my argument.
The following is from Tolkien himself in Appendix E of LOTR:
"C has always the value of k even before e and i: celeb ‘silver’ should be pronounced as keleb ."
Thus, when transcribing the Tengwar script into a Roman script, you do not use "k", you use "c."
It is not "Rike", it is "Ricë."
Both c and k denote the same sound [k] in Tolkien's Quenya writings. In his esssays, notes, he mostly used k, only for the printed published works did he switch to c. Both spellings are valid, and I happen to prefer k. That's all.
Same with ë - its only function in LotR is to remind his English speaking readers that those e-s are not silent. He rarely used them elsewhere.