Lightening or darkening a colour by changing lightness alone (rather than also drifting its saturation or hue) is the most reliable way to get a paler or deeper version that still reads as 'the same colour' — this is the tint/shade relationship described in the glossary.
Practical advice
Adjust My Colour's 'lighter' and 'darker' options change lightness specifically, at three strengths, so the family relationship to the original colour stays recognisable.