The answer is between you and your customer. Some applications require a very close color match other do not.
Total color difference (delta e) < 1.0 is considered a good color match. However, many customers will specify tolerances on each of the three color attribute; L, a, and b, for example a customer may specify delta L < 0.25, delta a < 0.25, and delta b < 0.25. This would result in a total delta e < 0.43. Calculation: Delta e = ((delta L2) + (Delta a2) + (delta b2)) 1/2
A delta e of < 0.5 is a fairly tight tolerance; a delta e of < 1.0 is usually adequate. Most untrained people have an eye able to distinguish a total color difference of 1.0 (delta e). At 0.5 delta e, only a trained colorist can detect the difference.
Color matching between two labs always depends on the sample color (on some samples, color differences are easier to judge), surface texture of the sample, the base resin, and the type of instrument used to measure the sample color. This can be quite complicated. Therefore, the first step is to have you and your customer agree on a match, then discuss the color tolerances or deviation fromm that match which will cause him or her problems in production. You might vary your agreed upon match + or - small quantities of the pigment and send them to him for discussion.