Context. The Lyman α Reference Sample (LARS) of 14 star-forming galaxies offers a wealth of insight into the workings of these local analogs to high-redshift star-forming galaxies. The sample has been well-studied in terms of Lyα and other emission line properties, such as H I mass, gas kinematics, and morphology. Aims. We analyze deep surface photometry of the LARS sample in UBIK broadband imaging obtained at the Nordic Optical Telescope and the Canada-France-Hawaii Telescope, and juxtaposition their derived properties with a sample of local high-redshift galaxy analogs, namely, with blue compact galaxies (BCGs). Methods. We construct radial surface brightness and color profiles with both elliptical and isophotal integration, as well as RGB images, deep contours, color maps, a burst fraction estimate, and a radial mass-to-light ratio profile for each LARS galaxy. Standard morphological parameters like asymmetry, clumpiness, the Gini and M20 coefficients are also obtained and analyzed, as well as isophotal asymmetry profiles for each galaxy. In this context, we compare the LARS sample to the properties of the BCG sample and highlight the differences. Results. Several of these diagnostics indicate that the LARS galaxies have highly disturbed morphologies even at the level of the faintest outer isophotes, with no hint at a regular underlying population, as found in many BCG sample galaxies. The ground-based photometry reaches isophotes down to ~28 mag arcsec⁻², while the space-based data reach only ~26 mag arcsec⁻². The ground-based observations therefore reveal previously unexplored isophotes of the LARS galaxies. The burst fraction estimate suggests a spatially more extended burst region in LARS than in the BCGs. Comparison to stellar evolutionary models in color–color diagrams reveals complex behavior of the radial color profiles, often inconsistent with a single stellar population of any age and metallicity, but instead suggesting a mixture of at least two stellar populations with a typical young mass fraction in the range 0.1–1%. Conclusions. The galaxies in the LARS sample appear to be in earlier stages of a merger event compared to the BCGs. Standard morphological diagnostics like asymmetry, clumpiness, Gini and M20 coefficients cannot separate the two samples, although an isophotal asymmetry profile successfully captures the average difference in morphology. These morphological diagnostics do not show any correlation with the equivalent width or the escape fraction of Lyman Alpha.