  The unified correspondence theory for distributive lattice expansion logics
(DLE-logics) is specialized to strict implication logics. As a consequence of a
general semantic consevativity result, a wide range of strict implication
logics can be conservatively extended to Lambek Calculi over the bounded
distributive full non-associative Lambek calculus (BDFNL). Many strict
implication sequents can be transformed into analytic rules employing one of
the main tools of unified correspondence theory, namely (a suitably modified
version of) the Ackermann lemma based algorithm $\msf{ALBA}$. Gentzen-style
cut-free sequent calculi for BDFNL and its extensions with analytic rules which
are transformed from strict implication sequents, are developed.
