The problem is linux shell does its own interpolation
Yes, Anonymous Monk - you were spot-on in your analysis.

Here is why: 
$ a="Hello"

$ echo $a
Hello

$ echo "$a"
Hello

$ echo '"$a"'
"$a"

$ echo "'"$a"'"
'Hello'

$ echo ""'"$a"'""
"$a"

[download]
For the actual solution to my problem, this means: 
    my $command = qq/egrep "'"^$lemma:"'" \/home\/lexicon/;

    my $lexical_entry = `$command`;

[download]

Thanks to all those who were willing to help. Your effort to respond is much appreciated.

Thanks for leading me towards the actual solution!

Cheers - Pat

In reply to Re^2: How to include a doublequoted string into a backticked expression? by pat_mc
in thread How to include a doublequoted string into a backticked expression? by pat_mc

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