This doesn't really need a pattern but I felt like writing up the recipe anyway.
With bulky yarn and suitable needles, cast on 5 stitches (or as many as needed to fit around your tube of lip balm) and knit in garter stitch for about 7 inches (or until it will fit, slightly stretched, lengthwise around your tube of lip balm). Cast off. Fold ends towards center and sew the sides together.
In one corner, pick up three stitches. Knit i-cord for 1 1/2 inches (or as long as necessary to make a loop). With keyring on i-cord, sew down the end to the cozy to make a loop.
Adapt as you like. Knit in stockinette or in sock yarn and with a lacy pattern. This cozy is smaller than a swatch, so go ahead, be daring!