As describe here, you configure loggers in Liberty by something like this in the server.xml:
<logging traceSpecification="*=audit:com.myco.mypackage.*=debug"/>
and see the logging metatype doc to configure other aspects like log file size, number of logs to keep, etc.
Or, as the article mentions, you can use the bootstrap.properties
entries to do the same, e.g. com.ibm.ws.logging.trace.specification.
Though WebSphere also supports java.util.logging APIs, its full infrastructure isn't necessarily configured the same way as say Tomcat, which your app may be patterned after.
If you want to configure different logging behavior for different applications you can have the application Java code use a different Logger name for each, and then configure them differently through the single server.xml config (or also potentially separate the apps out onto different servers).
Dynamically changing the trace settings on a running server can be done simply by editing the server.xml config (as can dynamically configuring almost any aspect of Liberty).