We report a transverse-field muon-spin rotation/relaxation (μSR) study of the internal-field distribution in the mixed state of LaFeAsO_(0.89)F_(0.11) and LaFeAsO_(0.75)H_(0.25), representative of the first (SC1) and second (SC2) superconducting domes of the LaFeAsO₁₋ₓMₓ (M=rm F,H) family, respectively. Below the superconducting transition temperature T_(rm c), the linewidth of the internal-field distribution increases in both samples, indicating the formation of a vortex lattice. Above T_(rm c), the linewidth remains field dependent and increases approximately linearly with field, consistent with broadening of the powder spectrum caused by an anisotropic Knight shift. After subtraction of this normal-state contribution, the superconducting linewidth σ_(rm sc) exhibits qualitatively different field dependences in the two samples. At 4K, the SC1 (x_(rm F)=0.11) sample shows the expected monotonic decrease with increasing field, whereas the SC2 (x_(rm H)=0.25) sample develops a pronounced local maximum near 3T. A contour representation of σ_(rm sc)(T,H) further reveals a ridge of local maxima whose field position, H_(σ,max)(T), shifts to lower fields upon warming and disappears near T_(rm c). The anomalous field evolution observed in the SC2 sample is consistent with an additional field-induced contribution associated with enhanced Pauli-paramagnetic effects, highlighting the distinct electronic character of the two superconducting domes.