How to do an if statement from the result of an executed command

Use the bash [[ conditional construct and prefer the $(<command>) command substitution convention. Additionally, [[ prevents word splitting of variable values therefore there is no need to quote the command substitution bit..

if [[ $(netstat -lnp | grep ':8080') = *java* ]]; then
  echo "Found a Tomcat!"
fi

Another alternative is to simply test the exit status of grep itself, which will return false (1) if there was no match and true (0) if there was one, by not using the [ command.

if netstat -lntp | grep ':8080.*java' > /dev/null; then
    echo "Found a Tomcat!"
fi

The redirection to /dev/null is to prevent it from also printing the found line to the screen.

Even more simple,

netstat -lntp | grep ':8080.*java' > /dev/null && command

If you just want to do one thing.