Evaluating the Long-term Safety and Tolerability of Imatinib in Patients With Lymphangioleiomyomatosis (LAM)

Inclusion Criteria: * Women 18 through 64 years of age (inclusive) * Pulmonary Function Test (PFT) with following criteria: 1. DLCO \>20% predicted and FVC \<90% OR 2. Post bronchodilator FEV1 between 30% and 90% predicted. * Confirmed or possible diagnosis of LAM * Willing to avoid grapefruit juice and St. John's wort while in the study * Able and willing to comply with the study procedures Exclusion Criteria: * Women who have or will undergo a transplant * Women who will undergo surgery * Women who are currently pregnant or plan on a pregnancy * Women who are currently breast feeding or lactating * Dementia or other cognitive dysfunction that, in the opinion of the investigator, would prevent the participant from consenting to the study or completing study procedures * Currently taking any of the following medications: * Antifungal Medications: Ketoconazole; Itraconazole ; Voriconazole. * Antibiotics for bacterial infections: Clarithromycin. * Analgesics to treat headaches/migraines: Dihydroergotamine; Dihydroergotamine intranasal * Antiretroviral protease inhibitors used in human immunodeficiency virus (HIV) infections: Atazanavir ; Nelfinavir; Indinavir; Ritonavir; Saquinavir * Anti-epileptic or seizure medications: Carbamazepine, Fosphenytoin; Oxcarbamazepine; Phenobarbital ; Phenytoin; Primidone * Anti-depressant medications: Nefazodone; St. John's wort * Targeted cancer drugs: Regorafenib; Venetoclax ; Cobimetinib * Ivabradine (used to treat chronic heart failure); Telithromycin (used to treat community acquired pneumonia); Lomitapide (treatment of familial hypercholesterolemia); Lonafarnib (Hutchinson-Gilford progeria syndrome); conivaptan (treat low sodium levels); flibanserin (management of hypoactive sexual desire disorder (HSDD)); Naloxegol (opioid-induced constipation); Warfarin (prevent blood clots); Lurasidone (schizophrenia and bipolar depression); Eliglustat (treatment of Gaucher's disease). * Non English speaking, illiterate, or other vulnerable persons will not be included among study subjects. * Any condition that in the opinion of the investigator might adversely influence the study outcome.