There are other threads/posts about this already. Please use the forum search before posting new threads. Searching for LibAddonMenu or LAM would have provided them easily.
But basically you need to use the "reference" tag of the lam options to give it a name you can reference to.
And then use <referenceVariableOfDropdownBox>:UpdateChoices(listOfChoices, choicesValues, choicesTooltips)
choicesValues and choicesTooltips are optional. But I'd at least always provide choices and choicesValues so that the getfunc and setFunc uses the choicesValues easily, instead of having to check all entries in choices to match the string of your getFunc/setFunc parameter!
Searching for LAM or UpdateChoices (you could not know the later until now I assume :-)) will give you example forum threads, e.g.
https://www.esoui.com/forums/showthr...=UpdateChoices
I've added it to the Wiki as well now:
https://wiki.esoui.com/LibAddonMenu:...wn_box_entries