A variety of conditions can cause brown pigmentation on the lower legs. It would be advisable to have a doctor have a look at it for proper assessment.
Eczema on its own could worsen the condition and possibly leave dark marks known as Post Inflammatory Hyperpigmentation (PIH).
Best way to go about it would be to keep the eczema under control with the use of moisturizers and/ steroid creams.
Depending on the cause of the brown pigmentation, it can typically be treated by:
- Lightening creams
- Q- Switch Lasers
Hope this helps! š