Investigation of Cognitive Outcomes With Cannabidiol Oral Solution

Key Inclusion Criteria: * Participant is male or female aged 3-10 years. * Participants' parent(s)/legal representative is willing and able to give informed consent for participation in the trial; where the participant possesses adequate understanding, informed assent should also be taken. * Participant and their caregiver are willing and able (in the investigator's opinion) to comply with all trial requirements. * Participant must have a clinical diagnosis of Lennox-Gastaut Syndrome (LGS), with onset within the last 5 years. This includes certification from the investigator of prior electroencephalogram (EEG) documenting slow spike wave (\< 3 Hertz \[Hz\]) during the participant's history and evidence of more than 1 type of generalized seizure, including drop seizures (atonic, tonic, or tonic-clonic), for at least 6 months. * Investigator can confirm that the addition of GWP42003-P to the participant's existing antiepileptic drug (AED) regimen is warranted. * Participant must have at least 1 drop seizure each week during the first 28 days of the baseline period. * A minimum level of general intellectual functioning as assessed at screening with the Peabody Picture Vocabulary Test * Participant's parent(s)/legal representative is willing to allow the responsible authorities to be notified of participation in the trial, if mandated by local law. * Participant's parent(s)/legal representative is willing to allow his or her primary care practitioner (if they have one) and consultant (if they have one) to be notified of participation in the trial, if the primary care practitioner/consultant is different to the investigator. Key Exclusion Criteria: * Participant has clinically significant unstable medical conditions other than epilepsy. * Participant experiences \> 300 total seizures within the first 28 days of the baseline period. * Participant has any prior exposure to GWP42003-P. * Participant has initiated felbamate within the last 12 months. * Participant has initiated mammalian target of rapamycin (mTOR) inhibitors for epilepsy within the last 4 weeks. * Participant is currently using or has in the past used recreational or medicinal cannabis or synthetic cannabinoid-based medications (including Sativex®) within the 3 months prior to trial entry. * Participant has had clinically relevant symptoms or a clinically significant illness, other than epilepsy, in the 4 weeks prior to screening or Visit 2. * Participant has laboratory values at screening or Visit 2 that are clinically significantly abnormal in the investigator's opinion. * Participant tests positive for Δ9-tetrahydrocannabinol (THC) or cannabidiol (CBD) at screening. * Participant has any known or suspected hypersensitivity to cannabinoids or any of the excipients of GWP42003-P. * Participant has significantly impaired hepatic function at the screening visit, defined as any of the following: * Serum alanine aminotransferase (ALT) or aspartate aminotransferase (AST) \> 5 × upper limit of normal (ULN); * Serum ALT or AST \> 3 × ULN and (total bilirubin \[TBL\] \> 2 × ULN or international normalized ratio \[INR\] \> 1.5); * Serum ALT or AST \> 3 × ULN with the presence of fatigue, nausea, vomiting, right upper quadrant pain or tenderness, fever, rash, and/or eosinophilia (\> 5%). * Participant has received an investigational medical product within the 3 months prior to the screening visit. * Participant has any other significant disease or disorder, which, in the opinion of the investigator, may either put the participant at risk because of participation in the trial, may influence the result of the trial, or may affect the participant's ability to take part in the trial. * Any abnormalities identified following a physical examination of the participant that, in the opinion of the investigator, would jeopardize the safety of the participant if he/she took part in the trial * Participant has been previously enrolled into this trial.