Style:
Function prototype should go after the macros:

extern int lkpi_sysctl_handle_charp(SYSCTL_HANDLER_ARGS);

I also like to use extern, though some see it redundant.

Just use the Linux allocator, kalloc(GFP_KERNEL) ?

The function is very small and leaks are impossible!

Take this lock exclusively right here. Otherwise SYSCTL_IN and SYSCTL_OUT gets a great chance to see different versions of *charp when try_upgrade is failed

SYSCTL_OUT can sleep. You should call sysctl_wire_old_buffer() before taking lkpi_charp_lock

You cannot do malloc(M_WAITOK) with non-sleepable lock held.

How these operations on *charp are synchronized with drm-kmod? Are they protected by external lock?

In the kmods we have, charp parameters are only used for boot-only tunables. I'm not sure if they even make sense with things that can change at runtime. There is no synchronization, the module just expects the kernel to modify the pointer on load and reads it when initializing the hardware.

var must be freed on module unload

IMO charp should be freed only after successfull SYSCTL_IN(). I think *charp should not be reseted after e.g. EFAULT

Ok. It looks that drm-kmod is awared of absence of synchronization and does strdup() before parsing of data referenced by charp.

hmm well, I put it here because if (req->newlen == 0) I replace it with NULL without doing SYSCTL_IN

This kfree() looks incorrect. Should be kfree(var); ???