When the activated ability resolves, Transmogrifying Licid becomes an Aura enchantment and ceases to be either a creature or an artifact. Since it is no longer a creature, it also loses the creature type Licid. When the effect is ended, it goes back to being an artifact creature with the creature type Licid and ceases to be an Aura enchantment.

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.

The enchanted creature gains the artifact type in addition to any other card types it may already have.

If the permanent it is on was only a creature due to an effect, when that effect ends, the Licid will find itself enchanting something illegal and be put into the graveyard.