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We present a $L$-band (2.98--3.96$μ$m) spectroscopic study of 8 young L dwarfs with spectral types ranging from L2 to L7. Our spectra ($λ/{Δλ}\approx$ 250 to 600) were collected using the Gemini Near-InfraRed Spectrograph. We first examine the young $L$-band spectral sequence, most notably analyzing the evolution of the $Q$-branch of methane absorption feature at 3.3 $μ$m. We find the $Q$-branch feature first appears between L3 and L6, as previously seen in older field dwarfs. Secondly, we analyze how well various atmospheric models reproduce the $L$-band and published near-IR (0.7--2.5 $μ$m) spectra of our objects by fitting five different grids of model spectra to the data. Best-fit parameters for the combined near-IR and $L$-band data are compared to best-fit parameters for just the near-IR data, isolating the impact that the addition of the $L$-band has on the results. This addition notably causes a $\sim$100 K drop in the best-fit effective temperature. Also, when clouds and a vertical mixing rate ($K_{\mathrm{zz}}$) are included in the models, thick clouds and higher $K_{\mathrm{zz}}$ values are preferred. Five of our objects also have previously published effective temperatures and surface gravities derived using evolutionary models, age estimates, and bolometric luminosities. Comparing model spectra matching these parameters to our spectra, we find disequilibrium chemistry and clouds are needed to match these published effective temperatures. Three of these objects are members of AB Dor, allowing us to show the temperature dependence of the $Q$-branch of methane.