Paying the cost to end the effect is a special action and can't be responded to.

If a spell that can target enchantments but not creatures (such as Clear) is cast targeting the Licid after it has become an enchantment, but the Licid's controller pays the cost, the Licid will no longer be an enchantment. This will result in the spell failing to resolve for having no legal targets.

It becomes an Enchantment - Aura and stops being all other permanent types.