It seems there might be a misunderstanding or a misinterpretation of the Lorentz transformation equation in your statement. The Lorentz transformation equations describe how coordinates and time intervals are related between two inertial frames of reference in special relativity.
The correct expression for the transformation of time, from the stationary frame (t) to the moving frame (t'), is given by the equation:
t' = γ(t - (vx/c^2))
In this equation, γ represents the Lorentz factor, which is defined as γ = 1/√(1 - (v^2/c^2)), where v is the relative velocity between the two frames, and c is the speed of light.
If x is very large, it does not imply that the time in the moving frame, t', will be in the past of the stationary frame. The sign of t' will depend on the sign of (vx/c^2), which is a product of the relative velocity v, the distance x, and the reciprocal of the square of the speed of light.
If (vx/c^2) is positive, it means the relative motion is in the same direction as the positive x-axis, and the moving frame's time t' will be "ahead" or in the future compared to the stationary frame's time t. Conversely, if (vx/c^2) is negative, the moving frame's time t' will be "behind" or in the past compared to the stationary frame's time t.
It's important to note that the Lorentz transformation equations are derived from the principles of special relativity and have been experimentally confirmed. They accurately describe how time and space coordinates are related between different inertial frames, allowing for consistent and covariant formulations of physical laws in the framework of special relativity.