We report the analysis of high temporal resolution ground and space based photometric observations of SZ Lyncis, a binary star one of whose components is a high amplitude $delta$ Scuti. UBVR photometric observations were obtained from Mt. Abu Infrared Observatory and Fairborn Observatory; archival observations from the WASP project were also included. Furthermore, the continuous, high quality light curve from the TESS project was extensively used for the analysis. The well resolved light curve from TESS reveals the presence of 23 frequencies with four independent modes, 13 harmonics of the main pulsation frequency of 8.296943$pm$0.000002 d$^{-1}$ and their combinations. The frequency 8.296 d$^{-1}$ is identified as the fundamental radial mode by amplitude ratio method and using the estimated pulsation constant. The frequencies 14.535 d$^{-1}$, 32.620 d$^{-1}$ and 4.584 d$^{-1}$ are newly discovered for SZ Lyn. Out of these three, 14.535 d$^{-1}$ and 32.620 d$^{-1}$ are identified as non-radial lower order p-modes and 4.584 d$^{-1}$ could be an indication of a g-mode in a $delta$ Scuti star. As a result of frequency determination and mode identification, the physical parameters of SZ Lyn were revised by optimizations of stellar pulsation models with the observed frequencies. The theoretical models correspond to 7500 K $le $T$_{rm eff}$ $le$ 7800 K, log(g)=3.81$pm$0.06. The mass of SZ Lyn was estimated to be close to 1.7--2.0 M$_odot$ using evolutionary sequences. The period-density relation estimates a mean density $rho$ of 0.1054$pm$0.0016 g cm$^{-3}$
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