Minecraft alpha 1.2.6 lags when loading new chunks. Anyway to tone down the lag?

How can I tone down the lag?

You can do the classic "allocate more RAM" mixed with a NORMAL or SHORT render distance. That way the game will load a small number of chunks at the time.

Just set -Xmx to the maximum RAM that you want to allocate for the game. As an example:

-Xmx512M # 512MB
-Xmx2G # 2GB

As far as I know, there is no OptiFine version available for Alphas, Betas or Snapshots.

Since this is an old version...

Yep, I did some testing with Alpha 1.2.6, Beta 1.5 and Release 1.12.2 and even my "light gaming capable" PC struggled to keep up. Looks like this version is not optimized for recent PCs.

This is my benchmark of the Alpha 1.2.6 (old_alpha a1.2.6):

Average framerate  :   70.1 FPS
Minimum framerate  :   19.7 FPS
Maximum framerate  :  122.9 FPS
1% low framerate   :    4.1 FPS
0.1% low framerate :    3.0 FPS

Just in case, a benchmark of the Beta 1.5 (old_beta b1.5):

Average framerate  :   81.2 FPS
Minimum framerate  :   39.6 FPS
Maximum framerate  :  157.7 FPS
1% low framerate   :   15.1 FPS
0.1% low framerate :   5.6 FPS

And a more recent game version, Release 1.12.2

Average framerate  :  126.5 FPS
Minimum framerate  :   43.8 FPS
Maximum framerate  :  222.9 FPS
1% low framerate   :   27.9 FPS
0.1% low framerate :   16.2 FPS

All of them used the same world and graphics settings (medium render distance and fast graphics preset) plus none of them were modified. The resolution used was 1366x768.

Lowering the render distance to 10 and capping max frame rate at 60 keeps most lag away for me. And I have an old ass Mac.

I had a similar issue, what worked for me was getting the Technic launcher and installing the old days modpack. It works fine in fullscreen mode and I played for about 2 hours with no lag at 120fps on a 2014 Mac Mini (8gb RAM).