  The escape fraction of LyC ionizing radiation $f_{LyC}^{esc}$ is crucial for
understanding reionization, yet impossible to measure at z $\gtrsim$ 5.3.
Recently, studies have focused on calibrating indirect indicators of
$f_{LyC}^{esc}$ at z $\sim$ 0.3, finding that Ly$\alpha$ is closely linked to
it. What is still unclear is whether the LyC - Ly$\alpha$ relation evolves with
redshift, and if Ly$\alpha$ is truly applicable as an $f_{LyC}^{esc}$ indicator
during the reionization epoch. In this study, we investigate seven $-21
\lesssim M_{UV} \lesssim -19$ gravitationally lensed galaxies from the BELLS
GALLERY survey at z $\sim$ 2.3. Our targets have rest-frame Ly$\alpha$
equivalent widths ranging from 10 \r{A} to 100 \r{A} and low dust content
($-2.5 \lesssim \beta \lesssim -1.9$), both indicative of high LyC escape.
Surprisingly, direct estimates of $f_{LyC}^{esc}$ using Hubble Space Telescope
imaging with F275W and F225W reveal that our targets are not LyC emitters, with
absolute $f_{LyC}^{esc}$ $\lesssim$ 6.5% at 3$\sigma$ significance (with two
sources having absolute $f_{LyC}^{esc}$(3$\sigma$) $\lesssim$ 10% and
$\lesssim$ 16%). The low $f_{LyC}^{esc}$, coupled with the high Ly$\alpha$
escape fraction and equivalent width could potentially be attributed to the
redshift evolution of the neutral hydrogen column density and dust content. Our
results challenge previous studies based on local samples, suggesting that the
extrapolation of z ~ 0 Ly$\alpha$-based LyC indirect estimators into the
reionization epoch might not be correct.
