  We give a general surgery formula for the Casson-Walker-Lescop invariant of
closed 3-manifolds, seen as the leading term of the LMO invariant, in a purely
diagrammatic and combinatorial way. This provides a new viewpoint on a formula
established by C. Lescop for her extension of the Walker invariant. A central
ingredient in our proof is an explicit identification of the coefficients of
the Conway polynomial as combinations of coefficients in the Kontsevich
integral. This latter result relies on general \lq factorization formulas\rq\,
for the Kontsevich integral coefficients.
