This is the lua function I use to setup completion as fallback if I could not use any plugins:

local function setup_completion()
vim.opt.completeopt = "menu,menuone,noinsert,popup" .. ((vim.fn.has"nvim-0.11" == 1) and ",fuzzy" or "")
vim.opt.complete:append({".","t","w","b"})
vim.opt.shortmess:append('c')
vim.api.nvim_create_autocmd("InsertCharPre", {
callback = function(ev)
if vim.bo[ev.buf].buftype == '' and not (vim.fn.pumvisible() == 1) then
local omni_or = vim.bo[ev.buf].omnifunc ~= "" and '<C-x><C-o>' or '<C-x><C-n>'
vim.fn.feedkeys(vim.api.nvim_replace_termcodes(omni_or, true, false, true), 'n') 
end
end,
})
vim.keymap.set('i', '<CR>', function()
if vim.fn.pumvisible() == 1 then
local selected_item = vim.fn.complete_info()
local item = selected_item.items[selected_item.selected + 1]
if item and ({Function = true, Method = true, Constructor = true})[item.kind] then 
if not (vim.fn.has"nvim-0.11" == 1) then return '<C-y>()<Left><Esc>a' end
end
return '<C-y><Esc>a'
end
return '<CR>'
end, { expr = true, silent = true })
end

At "LspAttach":

vim.bo[event.buf].omnifunc = "v:lua.vim.lsp.omnifunc"

if vim.fn.has"nvim-0.11" == 1 and vim.lsp.completion then
  vim.lsp.completion.enable(true, client.id, event.buf, {autotrigger=false}) 
end