  We used VLT/XShooter to target a sample of nearby analogs of Lyman Break
Galaxies (LBGs). These Lyman Break Analogs (LBAs) are similar to the LBGs in
many of their physical properties. We determine electron temperatures using the
weak [O III]4363 emission line, and determine the oxygen abundance (O/H) using
the direct and strong line methods. We show that the direct and strong line
abundances are consistent with established relations within ~0.2 dex. The
analogs have nitrogen-to-oxygen ratios (N/O) and ionization parameters (q) that
are, on average, offset with respect to typical local galaxies but similar to
galaxies at z ~ 2 and other analogs. The N/O and q excesses correlate with the
offsets observed in the strong line ratios, again similar to z ~ 2. The star
formation rate surface densities are consistent with the high electron density
and ionization, indicating that the interstellar medium (ISM) pressure is set
by feedback from the starbursts. For a given O/H, the apparent N/O excess
arises due to the offset in O/H with respect to the local mass-metallicity
relation. This can be explained by recent inflow of relatively metal-poor gas
which lowers O/H while leaving N/O unchanged. The difficulties in determining
even basic ISM parameters in these nearby analogs illustrates some of the
challenges we face at much higher redshifts, where similar rest-frame optical
diagnostics for large samples of galaxies can be accessed with JWST.
