Here are the details from apport-bug, as promised (copied from #1764211 because I had to use a different Launchpad account):

ProblemType: Bug
DistroRelease: Ubuntu 16.04
Package: xorg 1:7.7+13ubuntu3
ProcVersionSignature: Ubuntu 4.4.0-119.143-generic 4.4.114
Uname: Linux 4.4.0-119-generic x86_64
.tmp.unity_support_test.0:

ApportVersion: 2.20.1-0ubuntu2.15
Architecture: amd64
BootLog: /dev/sda1: clean, 257395/9510912 files, 1925432/38014720 blocks
CompizPlugins: No value set for `/apps/compiz-1/general/screen0/options/active_plugins'
CompositorRunning: compiz
CompositorUnredirectDriverBlacklist: '(nouveau|Intel).*Mesa 8.0'
CompositorUnredirectFSW: true
Date: Sun Apr 15 18:28:07 2018
DistUpgraded: Fresh install
DistroCodename: xenial
DistroVariant: ubuntu
EcryptfsInUse: Yes
ExtraDebuggingInterest: Yes
GpuHangFrequency: Several times a week
GpuHangReproducibility: Occurs more often under certain circumstances
GpuHangStarted: Immediately after installing this version of Ubuntu
GraphicsCard:
 Advanced Micro Devices, Inc. [AMD/ATI] RV516 [Radeon X1300/X1550 Series] [1002:7187] (prog-if 00 [VGA controller])
   Subsystem: PC Partner Limited / Sapphire Technology RV516 [Radeon X1300/X1550 Series] [174b:e020]
   Subsystem: PC Partner Limited / Sapphire Technology RV516 [Radeon X1300/X1550 Series] (Secondary) [174b:e021]
InstallationDate: Installed on 2017-07-24 (265 days ago)
InstallationMedia: Ubuntu 16.04.1 LTS "Xenial Xerus" - Release amd64 (20160719)
ProcEnviron:
 LANGUAGE=en_CA:en
 TERM=xterm-256color
 PATH=(custom, no user)
 LANG=en_CA.UTF-8
 SHELL=/bin/bash
ProcKernelCmdLine: BOOT_IMAGE=/boot/vmlinuz-4.4.0-119-generic root=UUID=fe381ac7-304a-4c28-b497-bdefa6602251 ro quiet splash vt.handoff=7
SourcePackage: xorg
Symptom: display
Title: Xorg freeze
UpgradeStatus: No upgrade log present (probably fresh install)
dmi.bios.date: 01/24/2007
dmi.bios.vendor: LENOVO
dmi.bios.version: 2JKT30AUS
dmi.board.name: LENOVO
dmi.chassis.vendor: LENOVO
dmi.modalias: dmi:bvnLENOVO:bvr2JKT30AUS:bd01/24/2007:svnLENOVO:pn8811BJ8:pvrThinkCentreM55:rvnLENOVO:rnLENOVO:rvr:cvnLENOVO:ct7:cvr:
dmi.product.name: 8811BJ8
dmi.product.version: ThinkCentre M55
dmi.sys.vendor: LENOVO
version.compiz: compiz 1:0.9.12.2+16.04.20160823-0ubuntu1
version.ia32-libs: ia32-libs N/A
version.libdrm2: libdrm2 2.4.83-1~16.04.1
version.libgl1-mesa-dri: libgl1-mesa-dri 17.2.8-0ubuntu0~16.04.1
version.libgl1-mesa-dri-experimental: libgl1-mesa-dri-experimental N/A
version.libgl1-mesa-glx: libgl1-mesa-glx 17.2.8-0ubuntu0~16.04.1
version.xserver-xorg-core: xserver-xorg-core 2:1.18.4-0ubuntu0.7
version.xserver-xorg-input-evdev: xserver-xorg-input-evdev 1:2.10.1-1ubuntu2
version.xserver-xorg-video-ati: xserver-xorg-video-ati 1:7.7.0-1
version.xserver-xorg-video-intel: xserver-xorg-video-intel 2:2.99.917+git20160325-1ubuntu1.2
version.xserver-xorg-video-nouveau: xserver-xorg-video-nouveau 1:1.0.12-1build2
xserver.bootTime: Sun Apr 15 17:45:51 2018
xserver.configfile: default
xserver.devices:
 input Power Button KEYBOARD, id 6
 input Power Button KEYBOARD, id 7
 input Dell Dell USB Keyboard KEYBOARD, id 8
 input USB Optical Mouse MOUSE, id 9
xserver.errors:

xserver.logfile: /var/log/Xorg.0.log
xserver.version: 2:1.18.4-0ubuntu0.7
xserver.video_driver: radeon