  Non-Fermi liquid behavior in some fermionic systems have attracted
significant interest in last few decades. Certain pyrochlore iridates with
stronger spin-orbit coupling strength have recently been added to the list.
Here, we provide evidence of such a non-Fermi liquid ground state in another
mixed valent metallic pyrochlore iridate Pb$_2$Ir$_2$O$_{7-\delta}$, through
the combined investigation of electronic, magnetic and thermodynamic properties
as a function of temperature ($T$) and applied magnetic field ($H$).
Resistivity measurement showed a linear temperature dependence down to 15~K
below which it shows $\rho \sim T^{3/2}$ dependence while magnetic
susceptibility diverges as $\chi$(T) $\sim$ $T^{-\alpha}$ ($\alpha < 1$) below
10~K. While a strong negative $\Theta_{CW}$ has been observed from Curie-Weiss
fitting, absence of any long range order down to 80~mK only indicates presence
of strong inherent geometric frustration in the system. Heat capacity data
showed $C_p$ $\sim$ $T\ln(T_0/T)$ + ${\beta}T^3$ dependence below 15~K down to
1.8~K. More importantly spin-orbit coupling strength by x-ray absorption
spectroscopy was found to be weaker in Pb$_2$Ir$_2$O$_{7-\delta}$ compared to
other pyrochlore iridates. In absence of any large moment rare earth magnetic
ion, Pb$_2$Ir$_2$O$_{7-\delta}$ presents a rare example of an irirdate system
showing non-Fermi liquid behaviour due to disordered distribution of Ir$^{4+}$
and Ir$^{5+}$ having markedly different strengths of spin-orbit coupling which
might offer a prescription for achieving new non-Fermi liquid systems.
