Is it possible to upgrade from Lion 10.7.5 straight to the latest Yosemite in one go?

Yes.

Upgrading to Yosemite

You can upgrade to Yosemite from Lion or directly from Snow Leopard. Yosemite can be downloaded from the Mac App Store for FREE.

Upgrading to Yosemite

To upgrade to Yosemite you must have Snow Leopard 10.6.8 or Lion installed. Download Yosemite from the App Store. Sign in using your Apple ID. Yosemite is free. The file is quite large, over 5 GBs, so allow some time to download. It would be preferable to use Ethernet because it is nearly four times faster than wireless.

OS X Mavericks/Yosemite- System Requirements

Macs that can be upgraded to OS X Yosemite

1. iMac (Mid 2007 or newer) - Model Identifier 7,1 or later

2. MacBook (Late 2008 Aluminum, or Early 2009 or newer) - Model Identifier 5,1 or later

3. MacBook Pro (Mid/Late 2007 or newer) - Model Identifier 3,1 or later

4. MacBook Air (Late 2008 or newer) - Model Identifier 2,1 or later

5. Mac mini (Early 2009 or newer) - Model Identifier 3,1 or later

6. Mac Pro (Early 2008 or newer) - Model Identifier 3,1 or later

7. Xserve (Early 2009) - Model Identifier 3,1 or later

To find the model identifier open System Profiler in the Utilities folder. It's displayed in the panel on the right.

Are my applications compatible?

See App Compatibility Table - RoaringApps.

I have an iMac with a model idenitifier of 10,1. I tried doing this exact upgrade but my computer is now stuck between the upgrade and the older version. When attempting to install I get the following error: "OS X could not be installed on your computer. File system verify or repair failed. Quit Installer to restart your computer and try again.” When I go to Startup Disk and choose my hard drive (Mac HD OS X 10.7.5) I get “You can’t change the startup disk to the selected disk. Startup Disk could not gather enough info on the selected disk.” So I cannot boot into either the new version nor the version currently on the disk. What can I do to fix this?