Just built a small program to automatically set Black Ops 3 to high priority in task manager. Even if you set it yourself it will resort back to low priority automatically. Should help with a lot of lag issues.

https://www.dropbox.com/s/lz5k9kw65elyoxq/BlackOps3BetaLagFix.exe?dl=0
Download Mirrors:
http://www.filedropper.com/blackops3betalagfix

Scan: https://www.virustotal.com/en/file/e7ebb6c1ec581d4c26b16c86550c67f93c2082843723eeb845704069c23a8cc1/analysis/1440881779/

Source code if you don't trust me and/or want to compile it yourself. You can compile it by putting the code into a .cs file and compiling it using csc.exe.
Help for that can be seen here: https://msdn.microsoft.com/en-us/library/78f4aasd.aspx?f=255&MSPPError=-2147217396

using System;
using System.Diagnostics;
using System.Threading;

namespace BlackOps3LagFix
{
class Program
{
static void Main(string[] args)
{
while (true)
{
while (Process.GetProcessesByName("blackops3").Length > 0)
{
Process myProc = Process.GetProcessesByName("blackops3")[0];
Console.WriteLine(myProc.PriorityClass);
myProc.PriorityClass = ProcessPriorityClass.High;
Thread.Sleep(5000);
}

Console.Clear();
Console.WriteLine("Please launch the Black Ops 3 Beta!");

Console.WriteLine("Compiled using csc.exe by Sir Det Rape.");
Thread.Sleep(1000);
}
}
}
}

Capping your FPS so it hardly changes can also help stop the stuttering. I capped mine to 120 so now it never changes which helped me get less lag.

Just go into the graphics settings on the menu and limit the frame rate.