logical volume group has very little free space (19mb) could this be causing my macbook pro to run very slowly

The LVG actually captures almost all of the HDD capacity. That 19 MBs is all that is left. But it has nothing to do with space on your hard drive being too little. Your actual drive is the one listed as the Logical Volume or LV.

Ways to help make a slow Mac faster

17 Reasons Why Your Mac Runs Slower Than it Should

Slow Mac Performance? This Article Solves It!

Fix slow start-ups in OS X | MacFixIt - CNET Reviews

6 Easy Tips to Speed Up OS X Yosemite on Your Mac

Avoid using any third-party software that claims to clean up your computer. Usually this software does more bad than good. Furthermore, you don't need it. Note that all computers will become slower over time even under normal use. Experienced users typically erase the hard drive and do a clean install from scratch at least once a year or whenever installing a major OS upgrade. Of course doing so also means you must maintain regular and multiple backups.

Add more RAM or cut back on the number of concurrently running applications and utilities. Remove unnecessary software such as anti-malware and software that promises to clean your Mac. Check for runaway processes: Runaway applications can shorten battery runtime, affect performance, and increase heat and fan acti… Also see:

Pre-Mavericks

Open Activity Monitor in the Utilities folder. Select All Processes from the Processes dropdown menu. Click twice on the CPU% column header to display in descending order. If you find a process using a large amount of CPU time (>=70,) then select the process and click on the Quit icon in the toolbar. Click on the Force Quit button to kill the process. See if that helps. Be sure to note the name of the runaway process so you can track down the cause of the problem.

Mavericks and later

Open Activity Monitor in the Utilities folder. Select All Processes from the View menu. Click on the CPU tab in the toolbar. Click twice on the %CPU column header to display in descending order. If you find a process using a large amount of %CPU, then select the process and click on the Quit icon in the toolbar. Click on the Force Quit button to kill the process. See if that helps. Be sure to note the name of the runaway process so you can track down the cause of the problem.

One Possible Cause for a Slow Computer

(Thanks to EtreSoft for this contribution.)

If you have a problem with a slow machine and are using Google Docs, then check if the Google Docs page is showing in top sites in your browser. Once it gets into Top Sites, you get a Safari Web Content process that slows down your entire machine, but you don't even get a window for it. That's the key point. The problem will not be definitively solved until you remove the Google Docs page from Top Sites.

[This has been modified for clarity and syntax by Kappy.]

I have this problem too. My LV is empty, but my LVG is down at 19mb, from 500gb. Is there a way to empty, or erase, the LVG?

Your problem, hardware or software, may not be exactly the same as that of the original poster of this older thread, and it can be very confusing for everybody if we try to answer more than one question in each thread, which can also result in you applying the wrong advice to your particular problem.

In order for us to give your problem our proper attention to try to solve it, would you kindly start your own thread, describing the trouble you are having in the fullest detail, including completing your details to show what Mac or iDevice you are using, what operating system, and what version of the application in question. Please remember to post in the forum relevant to your hardware or version of OS X. A full list of all the support forums is here:

http://discussions.apple.com/index.jspa