ΔE 21.5, loose: different enough that you should pick on purpose. Lilac Purple is noticeably darker, more saturated, cooler than Fulgrim Pink.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 22). Lilac Purple is noticeably darker, more saturated, cooler than Fulgrim Pink.
The same difference applies the other way round: Fulgrim Pink is noticeably lighter, 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 Fulgrim Pink on the colour wheel See Lilac Purple on the colour wheel
All matches: Fulgrim Pink equivalents · Lilac Purple equivalents