Can I put newer os on my 24" imac that has osx lion on it now

Back up your data, check the application compatibility table, click here, and if your iMac is a mid-2007 or newer model, then on the download link for Yosemite or El Capitan.

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It looks like there were four 24" iMacs that could run Lion:

• iMac (24-inch) – model ID iMac6,1. For this one. Lion is the end of the line.
• iMac (24-inch Mid 2007) – model ID iMac7,1
• iMac (24-inch Early 2008) – model ID iMac8,1
• iMac (24-inch Early 2009) – model ID iMac9,1

To check your Mac's hardware model name against this list, use About This Mac in the Apple () menu. You can check the model ID by pressing the System Report button in that dialog.