  The oxygen isotope ($^{16}$O/$^{18}$O) effect (OIE) on the pseudogap
(charge-stripe ordering) temperature $T^{\ast}$ is investigated for the cuprate
superconductor La$_{2-x}$Sr$_{x}$CuO$_{4}$ as a function of doping $x$ by means
of x-ray absorption near edge structure (XANES) studies. A strong $x$ dependent
and sign reversed OIE on $T^{\ast}$ is observed. The OIE exponent
$\alpha_{T^{\ast}}$ systematically decreases from $\alpha_{T^{\ast}} = -
0.6(1.3)$ for $x = 0.15$ to $\alpha_{T^{\ast}} = - 4.4(1.1)$ for $x = 0.06$,
corresponding to increasing $T^{\ast}$ and decreasing superconducting
transition temperature $T_{c}$. Both $T^{\ast}(^{16}{\rm O})$ and
$T^{\ast}(^{18}{\rm O})$ exhibit a linear doping dependence with different
slopes and critical end points (where $T^{\ast}(^{16}{\rm O})$ and
$T^{\ast}(^{18}{\rm O})$ fall to zero) at $x_{c}(^{16}{\rm O}) = 0.201(4)$ and
$x_{c}(^{18}{\rm O}) = 0.182(3)$, indicating a large positive OIE of $x_{c}$
with an exponent of $\alpha_{x_{c}} = 0.84(22)$. The remarkably large and
strongly doping dependent OIE on $T^{\ast}$ signals a substantial involvement
of the lattice in the formation of the pseudogap, consistent with a polaronic
approach to cuprate superconductivity and the vibronic character of its ground
state.
