Incorporating a header rewrite for security purposes

If you TESTSERVER(2) servers are defined as nodes and reachable via the LTM you could just do a rewite with a node selection rather than a redirect.

when HTTP_REQUEST {
    set req [string tolower [HTTP::uri]]
    if { $req starts_with "/lodi" } {
        node  8080
        HTTP::uri /lodi/home
    }
    elseif { $req starts_with "/walking"} { 
        node  8080
        HTTP::uri /BOB/CAT
    }
    pool Test_Svrtier_Pool
}

Also, I'm not quite sure why you had the

use pool Test_Svrtier_Pool

use