After failing to get acceptable graphics when trying to install Ubuntu 16.04 on a Lenovo TS140, I had success after installing the PCIE 2.0 graphics card Nvidia GeForce 210. It's been about a week. I seem to have a working solution with both sound and video coming out of the new video card's HDMI cable, except I don't think the Suspend function works.
Update 2017-03-11. I have sporadic problems with streaming music having static in it (like radio station static?). It is not on-and-off, but the music will play fine for an hour or more and then when it starts getting static in it, it doesn't stop. I'm very confused by this because I can switch to playing MP3s on my local machine and there is no problem.
My Lenovo Ts140 is from 2014 and I had been running Xubuntu 14.04 since that time. This worked the whole time with minor problems concerning the file browser Thunar. In one case, it was definitely Thunar that had a bug in which program sometimes crashed after renaming a file. This was an outstanding bug for about a year and made me think that Xubuntu wasn't being maintained as much as the standard version. During the end of use, I would also have problems with the file browser window not refreshing properly after renaming or other changes. I can't say if this was the software or waning support for the Intel graphics card...
When I installed Ubuntu 16.04, I was told that a proprietary Intel driver was being used, but the graphics choices were low and only at 4:3 aspect ratios. I tried with Ubuntu MATA 16.04 as well as the current Fedora release, but they all had problems with the graphics. I actually never got to testing the audio, so I can't speak to that.
I did a quick search and found that a reviewer at Amazon had used this graphics card successfully with linux. I obviously can't guarantee it will work for you, but it did work for me.
I did not get any sound off of the motherboard with this install. I used an HDMI cable to connect the graphics card to my monitor (Insignia model NS-24E730A12). I then used the same "mini phono" plug I had used in the motherboard and plugged it into the monitor's headphone output to get sound. It successfully feeds a 5.1 speaker system, but when you go to "Test Sound" in the Settings program, there is only regular stereo.
I did attempt to install the latest driver from Nvidia, but the install failed. I was trying to use the "old way" of getting to a terminal and turn off the graphics and it didn't work any more. The good news is that the automated install from Ubuntu works fine (except maybe suspend?). To make sure this is in use, you go to Settings... Software and Updates... Additional Drivers, OR just ask for extra software during install. Currently I am using "binary Ver 340.101 from nvidia-340 (tested)".
These pages have been updated for Ubuntu 16.04 and provide additional information to using Ubuntu Linux software. I list the general Linux Programs (Apps) for Common Computer Tasks that most home users would need on one page. Then, I have a collection of more technical articles on the Linux Home File-Server Notes page. Enjoy.