It might be better to ask since I know my paper and may show you the answer if it is there.

Einstein's cosmological constant is a constant in Einstein's equation that might have various values that then determine a particular Friedmann's solution of Einstein's equation. Assuming Λ = 0 produces as a solution a "cycloidal" universe that is expanding from the Big Bang singularity, decelerating all the time, and after reaching maximal radius, it is shrinking back to a singularity. It was a "standard model" before 1998. Between 1998 and 2000 the observations meant to measure the rate of deceleration to prove that cosmology is science and so it is able to predict something, revealed that the observations instead of decelerating expansion as predicted showed accelerating expansion. So Λ got adjusted to (8/3)π G ρ / c^2 according to the new hypothesis about the expansion of the uiverse. The value Λ = 4π G ρ / c^2 (which I'm using) produces a Friedmann solution that is stationary (a universe that is neither expanding nor contracting), so called "Einstein's universe", and this value of Λ is called "Einstein's value of Einstein's cosmological constant". Any ohter value i not "Einstein's value" however the cosmological constant is always "Einstain's cosmological constant".

I don't know what "light dilation" might mean. The "time dilation" has a meaning that the time slows down along the distance without specifying how. If it is "gravitational time dilation" it would be time dilation that is inversly proportional to square of distance and for this reason it can't simulate the Hubble redshift which is exponential with the distance. I didn't have any choice in specifying the character of the time dilation since I take it from conservation of energy and it produces automatically an exponential relation between the "time dilation" and the distance to the object that emits the light. Just as it is observed in the Hubble redshift and I named it "general time dilation" since it applies to any space that contains matter that curves that space. The effect produces an illusion of accelerating space expansion with Hubble constant H_o=c/R wher R is the radius of curvature of space (and dH/dt=-H_o^2/2, about as it is observed).