  We revisit the so-called "Three Squares Lemma" by Crochemore and Rytter
[Algorithmica 1995] and, using arguments based on Lyndon words, derive a more
general variant which considers three overlapping squares which do not
necessarily share a common prefix. We also give an improved upper bound of
$n\log_2 n$ on the maximum number of (occurrences of) primitively rooted
squares in a string of length $n$, also using arguments based on Lyndon words.
To the best of our knowledge, the only known upper bound was $n \log_\phi n
\approx 1.441n\log_2 n$, where $\phi$ is the golden ratio, reported by Fraenkel
and Simpson [TCS 1999] obtained via the Three Squares Lemma.
