My update finder is not giving me OX 10.9 or current. I am stuck in 10.7.5. How do I update?

Open the Mac App Store and try downloading Yosemite. If you get told it's incompatible, your computer is running the newest Mac OS X version it can.

Back up your data and check your applications for compatibility before upgrading. In particular, Mac OS X 10.7 and newer don't support PowerPC programs such as versions of Microsoft Office prior to 2008.

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10.7.5 is the latest and last update for Lion. You're confusing "update" with "upgrade." You would get upgrades from the the App Store's Featured tab in lieu of Updates.