  We report our extensive 57Fe-, 75As-, 139La-, and 1H-NMR studies of
La_{0.8}Y_{0.2}FeAsO_{1-y} (La_{0.8}Y_{0.2}1111) and
LaFeAsO_{1-y}H_{x}(La1111H), where doping yttrium (Y) and hydrogen (H) into
optimally doped LaFeAsO_{1-y} (La1111(OPT)) increases T_c=28 K to 34 and 32 K,
respectively. In the superconducting (SC) state, the measurements of
nuclear-spin lattice-relaxation rate 1/T_1 have revealed in terms of a multiple
fully gapped s_\pm-wave model that the SC gap and T_c in La_{0.8}Y_{0.2}1111
become larger than those in La1111(OPT) without any change in doping level. In
La1111H, the SC gap and T_c also increase slightly even though a decrease in
carrier density and some disorders are significantly introduced. As a
consequence, we suggest that the optimization of both the structural parameters
and the carrier doping level to fill up the bands is crucial for increasing T_c
among these La1111-based compounds through the optimization of the Fermi
surface topology.
