ΔE 21.8, loose: different enough that you should pick on purpose. Limelight is much more saturated, cooler than Mummified Grime.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 22). Limelight is much more saturated, cooler than Mummified Grime.
The same difference applies the other way round: Mummified Grime is much more muted, warmer.
ΔE is the colour difference between our two swatch estimates: under about 6 is close, over about 15 is loose. Real paints also differ in finish, coverage and how they thin, so test before you commit.
See Mummified Grime on the colour wheel See Limelight on the colour wheel
All matches: Mummified Grime equivalents · Limelight equivalents