Lathe "pecking" on X?

I have attempted programming a g-code to do a pecking action on the x-axis. Since this is a lathe it does not have a y axis and I keep getting an error. 
Is there a G-Code for pecking on a lathe?

Thanks in advance.

What do you mean by "pecking"?

It's also known as chip breaking in mill G-Code. G83 and G73
The cycle sets final depth (X), retract position (R), peck depth (Q), and feed rate (F) normally used for drilling process. It's also handy for breaking stainless steel instead of getting birds nests or for live lathe tooling. Since my setup utilizes a grinder, without a pecking cycle it can stall the grinder out.
Right now I have to program a "peck" cycle manually. An example of this is:
G1 X2.02 F1
G0 X2.01
G1 X2.03 F1
G0 X2.02
G1 X2.04 F1
G0 X2.03

No, there is no built-in version of this, but I have seen demonstrations of it on Youtube.

However, it should be relatively easy to configure with LinuxCNC using external offsets.

An example of using this is in this video:

The trick is to calculate the required offset based on a non-integer factor of the spindle rotational position. 
How many lobes per rev you would need is something that might need some consideration, and might depend on the working diameter. 

The closest HAL component to what you need is probably "relief,comp" here:
github.com/andypugh/HalComps/tree/main

Thank you very much. I will review this information.