  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}$
