Let me quote an excerpt from the page which I linked above
What are the system requirements for Java on my Mac?
Operating system requirements: For Java 7 and later versions, you will need an Intel-based Mac running Mac OS X version 10.7.3 (Lion) and above.
I can’t unfortunately test on 10.7, but on my old MacBook with MacOSX 10.9 Java 7 and GanttProject run just fine.
Why don’t you download Java Runtime and try yourself? It is free and takes just a couple of minutes.