I start Ubuntu 14.10 on this T440p(Feb, 2015), and step by step upgrade to 15.04, 15.10, and finally LTS 16.04.

Before HWE: (kernel 4.4)
MIC_MUTE(Fn+F4) works under X, only the led of it does not light properly(Don't know why, because my work mate who is using same Laptop and Ubuntu 16.04 4.4 kernel does not have this issue); But 4.4 kernel has a very annoying bug, the text console display will freeze after some time using;

After enable HWE: (kernel 4.8)
Text console freeze problem is fixed; But MIC_MUTE under X does not work; acpi_listen under X does NOT show anything for Fn+F4;
Under text console(Ctrl+Alt+F6 for my example), acpi_listen shows for Fn+F4:
$ acpi_listen
button/f20 F20 00000080 00000000 K

Below command can toggle MIC_MUTE correctly (on both kernel)
amixer set -c 1 Capture toggle

Do you think this maybe a bug for xserver or I mis-config something of xserver? Since my system on 4.4 kernel does not work properly too.
Oh, I have to mention, because I hate the T440p's clickpad(no physical buttons), I replace it with a newer module's touchpad which has physical buttons.
Maybe this confuse kernel/xserver to determine correct model of my laptop?

$ dpkg -l \*hwe\*
Desired=Unknown/Install/Remove/Purge/Hold
| Status=Not/Inst/Conf-files/Unpacked/halF-conf/Half-inst/trig-aWait/Trig-pend
|/ Err?=(none)/Reinst-required (Status,Err: uppercase=bad)
||/ Name Version Architecture Description
+++-====================================-=======================-=======================-================================================== ============================
ii linux-generic-hwe-16.04 4.8.0.44.16 amd64 Complete Generic Linux kernel and headers
ii linux-headers-generic-hwe-16.04 4.8.0.44.16 amd64 Generic Linux kernel headers
ii linux-hwe-tools-4.8.0-41 4.8.0-41.44~16.04.1 amd64 Linux kernel version specific tools for version 4.8.0-41
ii linux-image-generic-hwe-16.04 4.8.0.44.16 amd64 Generic Linux kernel image
ii linux-signed-generic-hwe-16.04 4.8.0.44.16 amd64 Complete Signed Generic Linux kernel and headers
ii linux-signed-image-generic-hwe-16.04 4.8.0.44.16 amd64 Signed Generic Linux kernel image
ii linux-tools-generic-hwe-16.04 4.8.0.41.12 amd64 Generic Linux kernel tools
un xorg-renamed-package-hwe-16.04 <none> <none> (no description available)
ii xserver-xorg-core-hwe-16.04 2:1.18.4-1ubuntu6.1~16. amd64 Xorg X server - core server
ii xserver-xorg-hwe-16.04 1:7.7+13ubuntu4~16.04.2 amd64 X.Org X server
un xserver-xorg-input-all-hwe-16.04 <none> <none> (no description available)
ii xserver-xorg-input-libinput-hwe-16.0 0.19.0-1ubuntu0.1~16.04 amd64 X.Org X server -- libinput input driver
un xserver-xorg-input-vmmouse-hwe-16.04 <none> <none> (no description available)
un xserver-xorg-input-wacom-hwe-16.04 <none> <none> (no description available)
ii xserver-xorg-legacy-hwe-16.04 2:1.18.4-1ubuntu6.1~16. amd64 setuid root Xorg server wrapper
ii xserver-xorg-video-all-hwe-16.04 1:7.7+13ubuntu4~16.04.2 amd64 X.Org X server -- output driver metapackage
ii xserver-xorg-video-amdgpu-hwe-16.04 1.1.2-1~16.04.1 amd64 X.Org X server -- AMDGPU display driver
ii xserver-xorg-video-ati-hwe-16.04 1:7.7.1-1~16.04.1 amd64 X.Org X server -- AMD/ATI display driver wrapper
ii xserver-xorg-video-fbdev-hwe-16.04 1:0.4.4-1build5~16.04.1 amd64 X.Org X server -- fbdev display driver
ii xserver-xorg-video-intel-hwe-16.04 2:2.99.917+git20160706- amd64 X.Org X server -- Intel i8xx, i9xx display driver
un xserver-xorg-video-mach64-hwe-16.04 <none> <none> (no description available)
ii xserver-xorg-video-nouveau-hwe-16.04 1:1.0.12-2~16.04.1 amd64 X.Org X server -- Nouveau display driver
ii xserver-xorg-video-qxl-hwe-16.04 0.1.4-3ubuntu3~16.04.1 amd64 X.Org X server -- QXL display driver
un xserver-xorg-video-r128-hwe-16.04 <none> <none> (no description available)
ii xserver-xorg-video-radeon-hwe-16.04 1:7.7.1-1~16.04.1 amd64 X.Org X server -- AMD/ATI Radeon display driver
ii xserver-xorg-video-vesa-hwe-16.04 1:2.3.4-1build2~16.04.1 amd64 X.Org X server -- VESA display driver
ii xserver-xorg-video-vmware-hwe-16.04 1:13.1.0-2ubuntu3~16.04 amd64 X.Org X server -- VMware display driver