[Ketho]

C_AuctionHouse.GetItemSearchResultInfo() returns the item link from a search result, e.g. when shift-clicking an item in the list

This (ugly example with timers) shows how you can get an item link from searching by item ID and level, while standing at the auction house

function PrintAuctionItemLink(itemID, itemLevel, itemSuffix)
    if AuctionHouseFrame and AuctionHouseFrame:IsShown() then
        local itemKey = C_AuctionHouse.MakeItemKey(itemID, itemLevel, itemSuffix)
        C_AuctionHouse.SearchForItemKeys({itemKey}, {})
 
        C_Timer.After(0.5, function()
            local firstResult = C_AuctionHouse.GetBrowseResults()[1]
            AuctionHouseFrame:SelectBrowseResult(firstResult)
        end)
 
        C_Timer.After(1, function()
            local info = C_AuctionHouse.GetItemSearchResultInfo(itemKey, 1)
            print(info.itemLink, (info.itemLink:gsub("|", "||")))
        end)
    end
end

/run PrintAuctionItemLink(4711, 54) -- item level 54
> "[Glimmering Cloak]"
> "|cff1eff00|Hitem:4711::::::::120:258:512:53:1:4277:120:::|h[Glimmering Cloak]|h|r"

/run PrintAuctionItemLink(55582, 116) -- Hiri'watha Greaves, item level 116

As to how you would generate an item link straight from an item ID and level, I have no idea
There is a lot of magic involved, especially with item suffixes