The short answer is, you can't, not without inaccuracies. That is because lat/lon is not a projection and is not cartesian. If your map is already Mercator (and you say it is), then you can use the following code --

my $h_img_dims   => {img_width => 200, img_height => 200};
my $h_map_bbox   => {map_minx => 2090491, map_miny => 482208, map_maxx
+ => 2224055, map_maxy => 587708};
my $h_new_center => {x => 200, y => 100}; # for pan right/East
#my $h_new_center => {x => 0, y => 100}; # for pan left/West
#my $h_new_center => {x => 100, y => 200}; # for pan bottom/South
#my $h_new_center => {x => 100, y => 0}; # for pan up/North


# Convert the mouse click to earth coordinates
my ($x, $y) = _pixel2earth(
  h_img_dims   => $h_img_dims,
  h_map_bbox   => $h_map_bbox,
  h_new_center => $h_new_center,
);
  
  
sub _pixel2earth {
  my (%args) = @_;
  
  my $h_img_dims   = $args{h_img_dims};
  my $h_map_bbox   = $args{h_map_bbox};
  my $h_new_center = $args{h_new_center};

  # Mouse clicks equivalent in earth coordinates
  return (
    $h_map_bbox->{map_minx} + ($h_new_center->{x} * ( ($h_map_bbox->{m
+ap_maxx} - $h_map_bbox->{map_minx}) / $h_img_dims->{img_width}  )),
    $h_map_bbox->{map_miny} + ($h_new_center->{y} * ( ($h_map_bbox->{m
+ap_maxy} - $h_map_bbox->{map_miny}) / $h_img_dims->{img_height} ))
  );
  
}
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If you want to display a rectangular image, but measure non-rect coordinates such as lat/lon, you will have to project on the fly. Look at Proj.4, or better yet, look at MapServer which can do the image generation for you as well.