This study is to test LHP588 in persons who have mild to moderate Alzheimer's disease (AD) who have shown progressive mental decline in the last year and who have P. gingivalis infection. P. gingivalis infection has been linked to the development of dementia. LHP588 is designed to target the P. gingivalis bacterium, to potentially help to halt or slow down the progression of AD and its symptoms. A saliva test will be done to determine P. gingivalis infection. Tests for AD include standard questionnaires such as MMSE and a blood test for pTau 217. Treatment will be blinded, meaning the participant and the doctor will not know if the participant is receiving LHP588 or placebo. The total time for participation in the study may be up to 64 weeks. This includes a screening period (to ensure the participant is suitable for the study and the study is suitable for the participant) of up to 12 weeks, a treatment period of up to 48 weeks, and a safety follow-up period of 4 weeks after the last dose of the study drug to check the participant's overall health. Treatment is a once-a-day capsule. Caregiver participation is required. The study requires the participant to visit the study center (with the caregiver) at least 20 times within 64 weeks (this does not include any unplanned visits that may be recommended by the study doctor). In addition, the study doctor or clinic staff will contact the participant via phone at least 1 time.