As Metallic Mimic enters the battlefield, choose a creature type.
Metallic Mimic is the chosen type in addition to its other types.
When you are asked to do something "As X enters the battlefield", you are doing it immediately before it enters. This does not use the stack; when Metallic Mimic resolves you choose a type and it enters as that type, triggering any appropriate ETBs, and no one can do anything in between you choosing the type and Mimic hitting the battlefield.
If it instead read:
When Metallic Mimic enters the battlefield, choose a creature type.
Then it would be a triggered ability; Metallic Mimic would enter the battlefield as a "Shapeshifter", this ability would be put on the stack, and when it resolved you'd get to choose a type (like "Human") and it would become that type. Thalia's Lieutenant's ability would not be triggered.