  We present an optical polarimetric study of a nearby star-forming region,
Lambda-Orionis, to map plane-of-the-sky magnetic field geometry to understand
the magnetized evolution of the HII region and associated small molecular
clouds. We made multi-wavelength polarization observations of 34 bright stars
distributed across the region. R-band polarization measurements focused on
small molecular clouds BRC 17 and BRC 18 located at the periphery of the HII
region are also presented. The magnetic field lines exhibit a large-scale
ordered orientation consistent with the Planck sub-mm polarization
measurements. The magnetic field lines in both the BRCs are found to be roughly
in north-south directions; however, a larger dispersion is noticed in the
orientation for BRC 17 compared to BRC 18. Using structure-function analysis,
the strength of the plane-of-the-sky component of the magnetic field is
estimated as $\sim$28 $\mu$G for BRC 17 and $\sim$40 $\mu$G for BRC 18. The
average dust grain size and the mean value of the total-to-selective extinction
ratio (R$_{V}$) in the HII region are found to be $\sim$0.51 $\pm$ 0.05 $\mu$m
and $\sim$2.9 $\pm$ 0.3, respectively. The distance of the whole HII region is
estimated as $\sim$392 $\pm$ 8 pc by combining astrometry information from GAIA
EDR3 for YSOs associated with BRCs and confirmed members of central cluster
Collinder 69.
