Infantile Hemangioma: Given the initial diagnosis of congenital hemangioma at multiple sites (nose, philtrum, upper lip, and back) and the MRI findings of a left parietal enhancing structure connecting to peripheral vessels, infantile hemangioma remains a strong consideration. These lesions are known to be more common and can have a varied presentation, including the potential for central nervous system involvement.

Port-Wine Stain: Although initially considered, the description and MRI findings might lean more towards a vascular tumor rather than a port-wine stain, which is typically a capillary malformation. However, it's still a consideration due to the initial presentation.
Arteriovenous Malformation (AVM): The MRI description of an enhancing structure connecting to peripheral vessels could suggest an AVM, especially if there's a concern for a vascular anomaly beyond a simple hemangioma.

Sturge-Weber Syndrome: This condition is characterized by a port-wine stain in the distribution of the trigeminal nerve, often associated with leptomeningeal angiomatosis. Given the facial involvement and the finding of a parietal lesion, this diagnosis is critical not to miss due to its implications for neurological and ophthalmological complications.
PHACE Syndrome: An acronym for Posterior fossa malformations, Hemangiomas, Arterial anomalies, Cardiac anomalies, and Eye abnormalities, this syndrome is a consideration in infants with large facial hemangiomas and could explain the presence of a parietal lesion if it's part of a broader vascular anomaly.

Kasabach-Merritt Syndrome: A rare condition associated with a vascular tumor (often a kaposiform hemangioendothelioma or tufted angioma) that leads to severe thrombocytopenia and coagulopathy. While less likely, it's a critical diagnosis to consider due to its high morbidity and mortality.
Lymphangioma: Although less common than hemangiomas, lymphangiomas could present as congenital lesions and might be considered, especially if there are atypical features or a lack of response to typical hemangioma treatments.

Regarding the causes of lip ulcers that could remove part of the lips, these might include:

Infection: Bacterial, viral, or fungal infections can cause ulcers.
Trauma: Physical injury to the lip.
Autoimmune Conditions: Conditions like pemphigus or lupus can cause ulcers.
Vascular Anomalies: As discussed, certain vascular anomalies could potentially lead to ulceration and tissue loss.
Neoplastic Conditions: Rarely, tumors could cause ulcers and destruction of lip tissue.