Lyman α blobs
Lyman alpha blobs (LABs) are huge (~0.1–1 million lightyears' scale) regions surrounding a galaxy or galaxy group, where we see a higher-than-average flux of Lyman alpha (or "Lyα", i.e. the $\lambda=1216\,\mathrm{Å}$ photon originating from the 2→1 transition of neutral hydrogen). The physical origin has been debated, but is thought to be Lyα emitted from the central galaxies (or a quasar) and scattered by the surrounding hydrogen, and/or produced locally either by numerous smaller galaxies or even accreting gas that cools. The Lyα flux is very low, typically falling below $\sim10^{-19}\,\mathrm{erg}\,\mathrm{s}^{-1}\,\mathrm{cm}^{-2}\,\mathrm{arcsec}^{-2}$ farther away than $\sim 10\,\mathrm{kpc}$ from the center.
Probing this spectroscopically can be done with VLT's MUSE, but not much lower than $10^{-18}$ cgs units (see e.g. Herenz et al. 2020). To probe the surface brightness profile out to large distances, one can instead stack multiple LABs (e.g. Steidel et al. 2011).
Lyman break galaxies
A Lyman break galaxy (LBG) is, formally, a galaxy detected due to its lack of flux blueward of the Lyman break at $\lambda=921\,\mathrm{Å}$. The physical reason is that photons of shorter wavelengths are able to ionize the surrounding hydrogen. Steidel (1996) revolutionized high-redshift astronomy with this technique, because you can take an image of a large field through different filters, and then look for a galaxy that is invisible in filters blueward of the (restframe) Lyman break. This is called the "drop-out technique".
At high redshifts where both the density and the neutral fraction of hydrogen is larger, the break is seen not at $\lambda=921\,\mathrm{Å}$, but at the Lyman alpha wavelength at $\lambda=1216\,\mathrm{Å}$. Galaxies with a Lyα break can also be found with the drop-out technique, and somewhat confusingly such galaxies are also occasionally referred to a "LBGs", but it's important to realize that the physics are different, and that the break occurs at a different wavelength.
The answer
So, LBGs are found because there is an underlying (stellar) continuum that is "broken" at a specific wavelength. In contrast, LABs are found by comparing broadband and narrowband images, looking for regions where there is an excess flux in the narrowband. There (usually) isn't any continuum to be broken in a LAB region.
So, if I understand your question correctly, the answer is no.