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No, $\Omega_{\Lambda,0}$ in Eq. (1) is truly a constant by definition (made a small edit to make this more clear). See the discussion around Eq. (1.3.120) in these lectures notes. I'm not sure what notes you're reading so I don't know if the author is considering a matter-dominated universe but this result is true in a universe where $\Omega_{\Lambda,0} \ne 0$