My script stops working when the player respawns/dies?

--|| SERVICES ||--
local RunService = game:GetService("RunService");
local Players = game:GetService("Players");

--|| VARIABLES ||--
local LeftRightConnections = { };

--|| HELPER FUNCTIONS ||--
local function Lerp(a, b, c)
    return a + (b - a) * c;
end

--|| PLAYER ADDED AND REMOVED EVENTS ||--
game.Players.PlayerAdded:Connect(function(Player)
    local Character = Player.Character or Player.CharacterAdded:Wait();
    local Humanoid = Character:WaitForChild("Humanoid");

    local HumanoidRootPart = Character.HumanoidRootPart;
    local Torso = Character.Torso;

    local RootJoint = HumanoidRootPart.RootJoint;
    local LeftHipJoint = Torso["Left Hip"];
    local RightHipJoint = Torso["Right Hip"];

    local Force = nil;
    local Direction = nil;
    local Value1 = 0;
    local Value2 = 0;

    local RootJointC0 = RootJoint.C0;
    local LeftHipJointC0 = LeftHipJoint.C0;
    local RightHipJointC0 = RightHipJoint.C0;

    LeftRightConnections[Player] = RunService.Stepped:Connect(function()
        Force = HumanoidRootPart.Velocity * Vector3.new(1, 0, 1);

        if Force.Magnitude > 2 then
            Direction = Force.Unit    
            Value1 = HumanoidRootPart.CFrame.RightVector:Dot(Direction);
            Value2 = HumanoidRootPart.CFrame.LookVector:Dot(Direction);
        else
            Value1 = 0;
            Value2 = 0;
        end;

        RootJoint.C0 = RootJoint.C0:Lerp(RootJointC0 * CFrame.Angles(math.rad(Value2 * 10), math.rad(-Value1 * 10), 0), 0.2);
        LeftHipJoint.C0 = LeftHipJoint.C0:Lerp(LeftHipJointC0 * CFrame.Angles(math.rad(Value1 * 10), 0, 0), 0.2);
        RightHipJoint.C0 = RightHipJoint.C0:Lerp(RightHipJointC0 * CFrame.Angles(math.rad(-Value1 * 10), 0, 0), 0.2);
    end);
end)

Players.PlayerRemoving:Connect(function(Player)
    if LeftRightConnections[Player] then
        LeftRightConnections[Player]:Disconnect();
        LeftRightConnections[Player] = nil;
    end;
end)

How do I make it so it continues to work when the player respawns? (its a server script just fyi)

You need to wrap the code in your connection to Players.PlayerAdded in a connection to Player.CharacterAdded as Player.CharacterAdded:Wait() is not enough in this situation, since the function connected to Players.PlayerAdded is only ran once for each player that joins (meaning Player.CharacterAdded:Wait() is only evaluated once for each player), however Player.CharacterAdded:Connect(function() ... end) will consistently fire every time their character is regenerated after they die.

You should also add a connection to Humanoid.Died so that you can disconnect from RunService.Stepped upon the player's death to prevent a memory leak (and also to prevent the script from erroring, since HumanoidRootPart will be destroyed when their model respawns)

Doc Links: Player.CharacterAdded, Humanoid.Died