Inclusion Criteria:  Male or female participants ages 14 years and older at the time of consent.  Participant must have a documented history of Lennox-Gastaut Syndrome, including:  Evidence of at least one type of generalized seizure (see below) Electroencephalogram (EEG) diagnostic criteria (abnormal background activity, slow spike-wave discharges (< 2.5 Hz), and/or paroxysmal fast activity during sleep), and Abnormal cognitive development.  Participants must have seizures not completely controlled by ASMs with the following criteria:  Onset of seizures at 11 years of age or younger History of multiple seizure types that must include tonic or tonic/atonic seizures as well as current countable seizures that result in fall/drop. Countable motor seizure types resulting in a drop that are eligible for inclusion are: Focal with clear, observable motor signs (i.e., automatisms, dystonic posturing, focal tonic stiffening) Secondarily generalized tonic clonic (evolving to bilateral convulsive seizure from focal seizure) Generalized tonic clonic convulsion Clonic (note bilateral: symmetric R and L), and/or Tonic/Atonic. All medication and/or interventions for epilepsy including ketogenic diet and vagus nerve stimulation (VNS) must have been stable for ≥ 30 days prior to screening and the participant is willing to maintain a stable regimen throughout the study. Note: The ketogenic diet and VNS treatments are not counted as an ASM throughout the study. The participant must be approved to participate by the PI after review of the medical history, baseline seizure calendars, and inclusion/exclusion criteria. The Independent Reviewer will confirm Lennox-Gastaut Syndrome diagnosis for each participant enrolled in the study. Seizure criteria of ≥ 4 countable seizures that result in a fall/drop (tonic-clonic, tonic, clonic, atonic, focal with observable motor signs) per 4-week Baseline period (Observation Phase). Participants should be on a stable regimen of ASMs ≥ 30 days prior to Visit 1 and generally in good health. Participant, parent, or LAR is able and willing to maintain an accurate and complete daily seizure calendar. Sexually active women of child-bearing potential (WCBP) must be using a medically acceptable method of birth control and have a negative urine pregnancy test at the screening visit. A WCBP is defined as a female who is biologically capable of becoming pregnant. A medically acceptable method of birth control includes intrauterine devices in place for at least 3 months, surgical sterilization, or adequate barrier methods (e.g., diaphragm and foam). Use of oral contraceptives in combination with another method (e.g., a spermicidal cream) is acceptable. In participants who are not sexually active, abstinence is an acceptable form of birth control and urine will be tested per protocol. Women who are of non-child-bearing potential, i.e., post-menopause, must have this condition captured in their medical history. Pregnant women are excluded from this study. Have participant, parent, or LAR available and willing to give written informed consent, after being properly informed of the nature and risks of the study and prior to engaging in any study-related procedures.  Exclusion Criteria:  Known sensitivity, allergy, or previous exposure to EPX-100 (clemizole HCl). Exposure to any investigational drug or device ≤ 90 days prior to screening or plans to participate in another drug or device trial at any time during the study. Seizures secondary to illicit drug or alcohol use, infection, neoplasm, demyelinating disease, degenerative neurological disease, or progressive central nervous system (CNS) disease, metabolic illness, recent anoxic episode within the last 6 months requiring resuscitation, or progressive degenerative disease. Concurrent use of drugs known to interfere with EPX-100, including moderate or severe inducers or inhibitors of CYP3A4/5/7. Specifically, concurrent use of carbamazepine, oxcarbazepine, phenytoin, gabapentin, phenobarbital, and/or fenfluramine are excluded. Subjects who are unable to agree to refraining from grapefruits and grapefruit juice during the study period. Refer to Appendix 1 for a list of prohibited drugs. Receiving concomitant therapy with: centrally-acting anorectic agents; monoamine oxidase (MAO) inhibitors; any centrally-acting drugs with clinically appreciable amounts of serotonin agonist or antagonist properties, including serotonin reuptake inhibition (SRIs, SSRIs). Also, systemic corticosteroids (inhaled steroids are allowed) and intravenous immunoglobulin (IVIG) may reduce seizure frequency, thus are excluded throughout the study. Has any medical condition that, in the PI's judgment, is considered to be clinically significant and could potentially affect participant safety or study outcome, including but not limited to: clinically significant cardiac disease (including angina, congestive heart failure, uncontrolled hypertension, history of arrhythmias, and/or clinical valvulopathy), renal, pulmonary, gastrointestinal, hematologic or hepatic conditions; or a condition that affects the absorption, distribution, metabolism, or excretion of drugs. Has an active suicidal plan/intent or have had active suicidal thoughts in the past 6 months or a suicide attempt in the past 3 years.