  We investigate questions related to the presence of primitive words and
Lyndon words in automatic and linearly recurrent sequences. We show that the
Lyndon factorization of a k-automatic sequence is itself k-automatic. We also
show that the function counting the number of primitive factors (resp., Lyndon
factors) of length n in a k-automatic sequence is k-regular. Finally, we show
that the number of Lyndon factors of a linearly recurrent sequence is bounded.
