The following study suggests that montelukast may have a small beneficial effect on Alzheimer's disease (in terms of somewhat slower decline in some areas):

Leukotriene receptor antagonist use and cognitive decline in normal cognition, mild cognitive impairment, and Alzheimer’s dementia

Leukotriene receptor antagonists (LTRAs) alleviate Alzheimer’s disease (AD) pathology and improve cognition in animal models; however, clinical evidence is limited. This study aimed to explore the associations between the use of LTRAs (montelukast or zafirlukast) and cognitive performance in people with normal cognition, mild cognitive impairment (MCI), or AD dementia. We hypothesized that LTRA use would be associated with better cognitive performance over time...

In people with AD dementia, LTRA use was associated with better performance over time on tests for psychomotor processing speed and language but not memory. These longitudinal associations support the hypothesis that LTRAs may warrant investigation as a potential target for AD treatment. The lack of association with cognition among people with normal cognition and MCI does not provide evidence to support a role of LTRAs in slowing cognitive decline among people with normal cognition or MCI, although a small but significant effect on clinical progression was seen in both AD dementia and MCI groups.

Here is a link to the full study, Larry.

https://alzres.biomedcentral.com/articles/10.1186/s13195-021-00892-7