I believe you’re mixing things here – you do not need the color metafield, you need value of the Color option.
So the code would be like:
{% assign le_products = product.metafields.custom.product_limited_edition %}
{% if le_products %}
{% for p in le_products.value %}
{% assign option = p.options_with_values | where: "name", "Color" | first %}
{% assign color = option.values | join: " " %}
{{ p.title }} - {{ color | capitalize }}
{% endfor %}
{% endif %}