iRule redirect to HTTPS - Logical Error

Well, that elseif as it's currently written will never match because you're converting the host to lowercase and then attempting to match it against a string with upper case characters (websiteROOT). I realize this is a sanitized iRule, but I just wanted to raise this point in case that is your issue. Try this one:

when HTTP_REQUEST {

if { [string tolower [HTTP::uri]] starts_with "/websiteA" } {
 pool pool_websiteA
} elseif { [string tolower [HTTP::uri]] starts_with "/websiteB" } {
 pool pool_websiteB
} elseif { [string tolower [HTTP::uri]] starts_with "/websiteC" } {
 pool pool_websiteC
} elseif { [string tolower [HTTP::uri]] starts_with "/websiteD" } {
 pool pool_websiteD
} elseif { [string tolower [HTTP::uri]] starts_with "/websiteE" } {
 pool pool_websiteE
}
 else {
  HTTP::redirect "https://[HTTP::host][HTTP::uri]"
 }
}