Monitor tomcat availability using iRule

Of course!! Have you looked up the documentation for monitors on your version of LTM?

Best practice is to check the Receive String for some specific content (not just HTTP status code).

Here's a simple v10 HTTP/1.0 example we use in our Tomcat containers;-

monitor mn_bpweb_mode.jsp {
    defaults from http
    recv disable "transition"
    recv "normal"
    send "GET /platform/mode.jsp\r\n\r\n"
}

We use that jsp file to take servers in/out of the pool - it gets deployed with the Tomcat packages.

Here's another example we use for another application just to show you a more complicated send string;-

monitor mn_mcms_author.mycms.com.au_http {
    defaults from http
    recv "Alive"
    send "GET /libs/granite/core/content/login/clientlib/healthcheck.html?a=b HTTP/1.1\r\nHost: author.mycms.com.au\r\nConnection: close\r\n\r\n"
}