Configure LazyNvim to search only within lines containing a regex

I'd like to configure a keymap which searches within lines which start with the word "class".

When I was using fzf.nvim I used to have something like this:

# "[F]ind [A]nywhere [C]lass
nnoremap <leader>fac :Rg '^ *class '

This would launch a nice hover window with the results already filtered for lines which start with the word "class" (allowed for some initial whitespace). Then I could further filter the list by typing.

Is there an equivalent to that when using LazNvim? I've set things up to use fzf-lua but I can't see any option for starting with an initial regex.

Interestingly, AI suggests this to me, which actually seems not to work:

return {
  "ibhagwan/fzf-lua",
  config = function()
    local fzf = require("fzf-lua")

    -- Optional: call setup if you want to customize fzf-lua globally
    fzf.setup({})

    -- Keymap: Search for class definitions in the current buffer
    vim.keymap.set("n", "<leader>fac", function()
      fzf.grep_curbuf({
        search = "^ *class ",
        prompt = "Class definitions> ",
        regex = true,
      })
    end, { desc = "Find class definitions in current buffer (fzf-lua)" })
  end,
}

If found a solution buried in this GitHub issue:

:lua FzfLua.live_grep({ search="^#+", no_esc=true })

I don't know whether no_esc is documented anywhere, but I spent a while looking for this option and didn't find it.

So in my case, my shortcut should look like this:

return {
  "ibhagwan/fzf-lua",
  keys = {
    -- Remove LazyVim's default <leader>sa mapping
    { "<leader>sa", false },
    {
      "<leader>sac",
      function()
        require("fzf-lua").live_grep({
          search = "^ *class ",
          prompt = "Class definitions> ",
          no_esc = true,
        })
      end,
      desc = "[s]earch [a]nywhere [c]lass",
    },
    {
      "<leader>sad",
      function()
        require("fzf-lua").live_grep({
          search = "^ *def ",
          prompt = "Function definitions> ",
          no_esc = true,
        })
      end,
      desc = "[s]earch [a]nywhere [d]ef",
    },
    {
      "<leader>shc",
      function()
        require("fzf-lua").grep_curbuf({
          search = "^ *class ",
          prompt = "Class definitions> ",
          no_esc = true,
        })
      end,
      desc = "[s]earch [h]ere [c]lass",
    },
    {
      "<leader>shd",
      function()
        require("fzf-lua").grep_curbuf({
          search = "^ *class ",
          prompt = "Function definitions> ",
          no_esc = true,
        })
      end,
      desc = "[s]earch [h]ere [d]ef",
    },
  },
}