I hope this question is suitable; this problem always bugs me. It is an issue of mathematical orthography.
It is good praxis, recommended in various essays on mathematical writing, to capitalize theorem names when recalling them: for instance one may write "thanks to Theorem 2.4" or "using ii) from Lemma 1.2.1" and so on.
Should these names be capitalized when they appear unnumbered? For instance which of the following is correct?
"Using the previous Lemma we deduce..." versus "Using the previous lemma we deduce..."
"The proof of Lemma 1.3 is postponed to next Section." versus "The proof of Lemma 1.3 is postponed to next section."