... a regex for grep -P that would show me lines which had, roughly, ^[one or more non-whitespace chars, which also do not form an IP address][one or more whitespace chars][zero or more chars][an IP address]

My 0.02USD. It's possible to rigorously express all the stated requirements as regexes. It's highly convenient to do so by building upon existing Perl modules such as Regexp::Common.

The requirement
    [one or more non-whitespace chars, which also do not form an IP address]
can be exactly expressed as
    my $S_not_IPv4 = qr{ (?! $RE{net}{IPv4}) \S }xms
for a single such character, and
    $S_not_IPv4+
(within a regex) as "one or more" such characters.

The requirements  [one or more whitespace chars] and  [zero or more chars] are exactly met by  \s+ and  .* respectively.

For
    [an IP address]
it's convenient to use  $RE{net}{IPv4} defined in Regexp::Common::net, but this regex has a subtlety: it intentionally does not include boundary conditions and so may match what might be considered a non-IPv4 string in certain circumstances:

c:\@Work\Perl\monks>perl -wMstrict -le
"use Regexp::Common qw(net);
 ;;
 print 'match' if '54321.2.3.45678' =~ m{ $RE{net}{IPv4} }xms;
"
match
[download]

The programmer must determine the proper match criteria for each circumstance. I have used a "loose" criterion in the  $S_not_IPv4 definition, and also have a tighter  $ip definition that would exclude the  '54321.2.3.45678' match above.

So finally:

c:\@Work\Perl\monks>perl -wMstrict -le
"use Regexp::Common qw(net);
 ;;
 my $ip         = qr{ (?<! \d) $RE{net}{IPv4} (?! \d) }xms;
 my $S_not_IPv4 = qr{ (?! $RE{net}{IPv4}) \S }xms;
 ;;
 for my $s (
   'ADMIN__SANDRO_DESK=\"123.45.78.90\"   #  ilcylic Desktop',
   '# ADMIN__SANDRO_DESK=\"123.45.78.91\"   #  ilcylic Desktop (old)',
   '# 06/06/15    SR    Chgd SANDRO 121.123.65.92',
   @ARGV,
   ) {
   my $match = $s =~ m{ \A $S_not_IPv4+ \s+ .* $ip }xms;
   printf qq{%8s '%s' \n}, $match ? 'MATCH' : 'no match', $s;
   }
"
no match 'ADMIN__SANDRO_DESK="123.45.78.90"   #  ilcylic Desktop'
   MATCH '# ADMIN__SANDRO_DESK="123.45.78.91"   #  ilcylic Desktop (ol
+d)'
   MATCH '# 06/06/15    SR    Chgd SANDRO 121.123.65.92'
[download]

It's a bit wordy, but still possible to express as a CLI one-liner. I think it can be said to exactly meet the stated requirements. It does so in Perl and not for grep, but that's life.