If a woman clearly wishes an item to be present for cosmetic reasons, then in some cases it may not be considered a chatzitzah.
So long as the dye is maintained well enough that you find it aesthetically pleasing when you immerse, there is no problem. Ideally, you would re-dye the eyelashes before each immersion (but not immediately before, lest there be dye adhering to the skin around the eye). Even better would be to forgo the dye or to opt for a permanent dye, which is more likely to remain as you desire.