  We analyze a sample of $z$-dropout galaxies in the CANDELS GOODS South and
UDS fields that have been targeted by a dedicated spectroscopic campaign aimed
at detecting their Ly$\alpha$ line. Deep IRAC observations at 3.6 and 4.5
$\mu$m are used to determine the strength of optical emission lines affecting
these bands at z$\sim$6.5-6.9 in order to i) investigate possible physical
differences between Ly$\alpha$ emitting and non-emitting sources; ii) constrain
the escape fraction of ionizing photons; iii) provide an estimate of the
specific star-formation rate at high redshifts. We find evidence of strong
[OIII]+H$\beta$ emission in the average (stacked) SEDs of galaxies both with
and without Ly$\alpha$ emission. The blue IRAC [3.6]-[4.5] color of the stack
with detected Ly$\alpha$ line can be converted into a rest-frame equivalent
width EW([OIII]+H$\beta$)=1500$^{+530}_{-440}\AA$ assuming a flat intrinsic
stellar continuum. This strong optical line emission enables a first estimate
of f$_{esc}\lesssim$20% on the escape fraction of ionizing photons from
Ly$\alpha$ detected objects. The objects with no Ly$\alpha$ line show less
extreme EW([OIII]+H$\beta$)=520$^{+170}_{-150}\AA$ suggesting different
physical conditions of the HII regions with respect to Ly$\alpha$-emitting
ones, or a larger f$_{esc}$. The latter case is consistent with a combined
evolution of f$_{esc}$ and the neutral hydrogen fraction as an explanation of
the lack of bright Ly$\alpha$ emission at z$>$6. A lower limit on the specific
star formation rate, SSFR$>$9.1$Gyr^{-1}$ for $M_{star}=2 \times 10^9
M_{\odot}$ galaxies at these redshifts can be derived from the
spectroscopically confirmed sample.
