Unless you're dealing with either fixed-size records or a pre-indexed text file, you don't really have much choice other than to scan through it ignoring the parts you're not interested in.

my $started = 0;
open(LVMINFO, '<', $filename);
while (<LVMINFO>) {
  $started = 1 if /^LV Name/;
  next unless $started;
  last if /--- Logical extents ---/;
  chomp;
  # Process
  # Process
  # Process
}
close(LVMINFO);
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