Are 32 bit programs less laggy than 64 bit?

The lag when using a music software program that uses software synths.
Is down to the mode you select for the sound card.

Using the default sound driver produces glitching and lagging.
During recording, or play back mode.

Or when you have a software synth running.
It is due to the latency or lag of the sound card mostly at playback.

If you look at the setup options for sound playback in Ableton
You will see a sound driver option of Asio sound driver or Asio v2 driver select this over the windows audio device.
for lower latency so you get less lag or stuttering of sound or any static type noise sound.

In the options you should also have support for multi processor support.
If you have a Cpu with more than two cpu cores enable this option to help reduce lag.

For software synth playing of sounds and playback of performances on your system.

You are better off sticking with a 64 bit version of the software over a 32 bit version.
And a 64 bit capable os is also better.

The key is how good your sound chip is and how low the latency of it is.
Pci-e based add in sound cards do much better with lower latency values, than an on board sound chip used on your motherboard.

The main cause of the lag or distortion to sounds being played or played back.
Along with the amount of cpu cores you enable for software synth playback.