Liquid Rhythm 1.4.5 requires at minimum Java 1.6 and at maximum Java 1.8 — Java 9 introduced changes to Java that are incompatible with Liquid Rhythm 1.4.5, and your operating system will use the highest available version of Java, so having Java 9 (and up) will cause Liquid Rhythm 1.4.5 to not run. (This is also a problem for some modes of operation in Liquid Music 1.7.0 + Liquid Rhythm 1.7.0 but has been solved by system-isolated Java bundling in Liquid Music 1.8.0 + Liquid Rhythm 1.8.0).
Liquid Rhythm 1.4.5 is both 32-bit and 64-bit compatible on both macOS and Windows. The version of Java you will need will correspond with the architecture of your DAW. You can have both 32-bit and 64-bit versions of Java installed simultaneously for maximum compatibility. On macOS it is required to have Apple's legacy Java 1.6 JRE installed (Java 1.6 is the last version of Java that Apple published their own version of, and is also the highest version of Java that offers 32-bit support on macOS), alongside whichever Java 1.7 or 1.8 you may desire for 64-bit support.