We present Keck/MOSFIRE and Keck/LRIS spectroscopy of A1689-217, a lensed (magnification ∼ 7.9), star-forming (SFR ∼ 16 M yr −1 ), dwarf (log(M * /M ) = 8.07−8.59) Lyα-emitter (EW 0 ∼ 138Å) at z = 2.5918. Dwarf galaxies similar to A1689-217 are common at high redshift and likely responsible for reionization, yet few have been studied with detailed spectroscopy. We report a 4.2σ detection of the electron-temperature-sensitive [O III]λ4363 emission line, the second such detection at z > 2, and use this line to directly measure an oxygen abundance of 12+log(O/H) = 8.06 ± 0.12 (∼ 1/4 Z ). Using the rest-optical emission lines, we measure A1689-217's other nebular conditions including electron temperature (T e ([O III]) ∼ 14,000 K), electron density (n e ∼ 220 cm −3 ) and reddening (E(B −V ) ∼ 0.39). We study relations between strong-line ratios and direct metallicities with A1689-217 and other galaxies with [O III]λ4363 detections at z ∼ 0 − 3.1, showing that the locally-calibrated, oxygenbased, strong-line relations are consistent from z ∼ 0 − 3.1. We also show additional evidence that the O 32 vs. R 23 excitation diagram can be utilized as a redshift-invariant, direct-metallicity-based, oxygen abundance diagnostic out to z ∼ 3.1. From this excitation diagram and the strong-line ratio − metallicity plots, we observe that the ionization parameter at fixed O/H is consistent with no redshift evolution. Although A1689-217 is metal-rich for its M * and SFR, we find it to be consistent within the large scatter of the low-mass end of the Fundamental Metallicity Relation.