How can I reduce client lag when firing a remote event multiple times?

I have developed a BETA version of a game, think of papers please, it's a loop of a random frame showing, detecting to keypresses, sending it off to the server, and moving a part, that loop repeats with a while true do loop.

Whenever the frame shows, the user can either press [F] or [G], and dependant on the information, it's either right or wrong. The problem is that I need to wait for the user to make the input so I used a remote event to tell the server when that input occurred, but it causes more lag each time it is fired, by around 3 loops in a lag spike is noticeable.

I thought of making the part movement client-side (because it is a single-player game) but I have no idea how to do that, and if it ever becomes a multiple-player game, that would not really be practical.

How can I repeat the loop indefinitely without lag spikes occurring?

This is the loop:

while true do
    tween_car_in()

    spawn_docs()

    user_input()

    choose_passport()

    check_option()

    destroy_docs()

    tween_car_out()

    reset_cycle()
end

This is the relevant function:

repeat
    rs.OptionPicked.OnServerEvent:Connect(function()
        chosen = true
        rs.OptionPicked:FireClient(player)
    end)
    wait(0.25)
until chosen == true

And this is the keypress detection:

user_input.InputBegan:Connect(function(key_input)
    if key_input.KeyCode == Enum.KeyCode.F and picked == false and script.Parent.Visible == true then
        --Irrelevant Code
        wait(2)
        game.ReplicatedStorage.OptionPicked:FireServer(true)
        --Irrelevant Code
    elseif key_input.KeyCode == Enum.KeyCode.G and picked == false and script.Parent.Visible == true then
        --Irrelevant Code
        wait(2)
        game.ReplicatedStorage.OptionPicked:FireServer(true)
        --Irrelevant Code
    end
end)