  The stretched diamond lattice material LiYbO2 has recently been reported to
exhibit two magnetic transitions ($T_{N1} = 1.1 K$, $T_{N2} = 0.45 K$) via
specific heat, magnetization, and neutron scattering measurements [Bordelon et
al., Phys. Rev. B 103, 014420 (2021)]. Here we report complementary magnetic
measurements down to T = 0.28 K via the local probe technique of muon spin
relaxation. While we observe a rapid increase in the zero-field muon
depolarization rate at $T_{N1}$, we do not observe any spontaneous muon
precession for $T < T_{N1}$, which is typically associated with long-range
magnetic ordering. The depolarization rate in the ordered state shows a
surprising sensitivity to magnetic fields applied along the initial spin
polarization direction. Using a simple one-dimensional model, we show that
these results are consistent with the unusual random-phase bipartite
incommensurate magnetic structure proposed by Bordelon et al. for the
intermediate temperature range $T_{N2} < T < T_{N1}$. We also find evidence for
temperature-independent magnetic fluctuations persisting to our lowest
temperatures, but no obvious signature of the transition or spontaneous muon
precession at and below TN2, respectively. This result is suggestive of quantum
dynamics within a highly degenerate ground state.
