If possible, use the same JRE major version at both index and search time. When upgrading to a different JRE major version, consider re-indexing.
Different Java versions may implement different versions of Unicode, which will change the way some parts of Lucene treat your text.
An (outdated) example: with Java 1.4, LetterTokenizer will split around the character U+02C6, but with Java 5 it will not. This is because Java 1.4 implements Unicode 3, but Java 5 implements Unicode 4.
The version of Unicode supported by Java is listed in the documentation of java.lang.Character class. For reference, Java versions after Java 11 support the following Unicode versions:
In general, whether you need to re-index largely depends upon the data that you are searching, and what was changed in any given Unicode version. For example, if you are completely sure your content is limited to the "Basic Latin" range of Unicode, you can safely ignore this.