By default, the HOME variable would be /home/vcap in the runtime container.
You would have to tweak the classpath setting inside the catalina.sh script (under app/.java-buildpack/tomcat/bin/catalina.sh) or the setclasspath.sh.
You can either create a link or copy the jar file from your webapp to another location and refer to it ahead of the tomcat classes. This would be lot more work.
Or
you can include the env variable JAVA_ENDORSED_DIRS to have additional setting that would point to your jar file (i believe endorsed would get loaded ahead of the classpath setting).
By default, tomcat setclasspath.sh script sets the endorsed dirs to be :
JAVA_ENDORSED_DIRS="$CATALINA_HOME"/endorsed
You can set it to be:
JAVA_ENDORSED_DIRS="$HOME/app/WEB-INF/lib/myUtility.jar:$HOME/app/.java-buildpack/tomcat/endorsed"
and call set-env just like for JAVA_OPTS