ΔE 22.5, loose: different enough that you should pick on purpose. Lipstick is more muted, cooler than Crimson.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 22). Lipstick is more muted, cooler than Crimson.
The same difference applies the other way round: Crimson is more saturated, 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 Crimson on the colour wheel See Lipstick on the colour wheel
All matches: Crimson equivalents · Lipstick equivalents