[SDPhantom]

Since all the code is doing is matching items to set names, the lookup table doesn't need to be so complicated to use. Here's my example. There can be more optimizations depending on how you want the tooltip to look.

local TransmogSets={
    {
        name="Mystic's Regalia (Recolor)",
        items={14090, 26008, 14094},
    },
    {
        name="Imperial Plate",
        items={31436, 30002, 12424, 12425, 12422, 12427, 12429},
    },
--  And so on ...
};
 
--  Lookup Table
local ItemSetNames={}; do
    for _,set in ipairs(TransmogSets) do--  Scan through all sets
        for _,itemid in ipairs(set.items) do--  Scan through items
--          Add set name to list in lookup table
            if not ItemSetNames[itemid] then ItemSetNames[itemid]={}; end
            table.insert(ItemSetNames[itemid],set.name);
        end
    end
 
--  Sorts set names
    for _,list in pairs(ItemSetNames) do table.sort(list); end
end
 
--  Tooltip Hook
GameTooltip:HookScript("OnTooltipSetItem",function(self)
    local _,link=self:GetItem();
    if not link then return; end--  Exit if we have no item
 
    local id=tonumber(link:match("|Hitem:(%d+)")) or 0;--   Force nil to zero if we have an invalid link (no items exist at index zero)
    if ItemSetNames[id] then
        for i,name in ipairs(ItemSetNames[id]) do
--          Only show our label on the first line
            self:AddDoubleLine(i<=1 and "Transmog Set:" or " ",name);
        end
    end
end);
 
--  Chat Hook
ChatFrame_AddMessageEventFilter("CHAT_MSG_LOOT",function(self,event,msg,...)
    local id=tonumber(msg:match("|Hitem:(%d+)")) or 0;--    Force nil to zero if we have an invalid link (no items exist at index zero)
    if ItemSetNames[id] then return false,msg.." (|cff9400d3Transmog Sets: "..table.concat(ItemSetNames[id],", ").."|r).",...; end
end);

Edit: Replaced string.join() section with more efficient table.concat() call.