ClearAll[a1, plot1, b1, plot2, f]
a1 = {{0.82, -109}, {0.98, -75}, {1.12, -57}, {1.17, -52}, {1.30,-43},
{1.37, -38}, {1.45, -34}, {1.54, -30}, {1.64, -26}, {1.76,-22.9}, {1.95,
-18.6}, {2.06, -16.6}, {2.24, -13.8}, {2.47, -11.2},{2.74, -8.9}, {3.09,
-6.8}, {3.53, -5}, {3.80, -4.17}, {4.12, -3.4},{4.59, -2.55}, {4.94, -2.06},
{5.26, -1.70}, {5.62, -1.37}, {5.83,-1.20}, {6.18, -0.96}, {6.51, -0.77},
{6.87, -0.58}};
plot1 = ListLinePlot[a1, PlotStyle -> Blue,PlotRange -> {{0, 7}, {15,-115}},
FrameLabel -> {{"ka",None}, {"Photon energy (eV)", "Ag"}}, Frame -> {{True,
False}, {True, True}},ImagePadding -> 70, ImageSize -> Large, FrameStyle ->
{{Blue, Black}, {Black, Black}},LabelStyle -> {14, GrayLevel[0]},FrameTicks
-> {{Transpose[{#, Map[PaddedForm[#, {3, 1}] &, #]}]&[Range[-120, 10, 20]],
Automatic}, {Transpose[{#, Map[PaddedForm[#, {2, 1}] &, #]}] &[Range[0, 7,
1.0]], Automatic}}]
b1 = {{0.82, 12.33}, {0.98, 7.06}, {1.12, 4.81}, {1.17, 4.19}, {1.30, 3.10},
{1.37, 2.66}, {1.45, 2.22}, {1.54, 1.87}, {1.64, 1.53}, {1.76, 1.24}, {1.95,
0.92}, {2.06, 0.78}, {2.24, 0.60}, {2.47, 0.45}, {2.74, 0.33}, {3.09, 0.23},
{3.53, 0.15}, {3.80, 0.12}, {4.12, 0.098}, {4.59, 0.071}, {4.94, 0.056},
{5.26, 0.047}, {5.62, 0.038}, {5.83, 0.034}, {6.18, 0.029}, {6.51, 0.024},
{6.87, 0.021}};
plot2 = ListLinePlot[b1, PlotRange -> {{0, 7}, {-2.0, 14}}, PlotStyle ->
Red, ImagePadding -> 70, ImageSize -> Large, FrameLabel -> {{None, "kb"},
{"Photon energy (eV)", None}}, Frame -> {{False, True}, {False, False}},
FrameStyle -> {{Black, Red}, {Black, Black}}, LabelStyle -> {14,
GrayLevel[0]}, FrameTicks -> {{Automatic, Transpose[{#, Map[PaddedForm[#,
{3, 1}] &, #]}] &[Range[-2, 14, 2.0]]}, {Automatic, Automatic}}]
f = Overlay[{plot1, plot2}]
Export["p5.tiff", Import[Export["p5.pdf", f, ImageSize -> 10,ImageResolution
-> 600]],ImageResolution -> 600]

Export["p5ZIP.tiff", f, ImageResolution -> 600, "ImageEncoding" -> "ZIP"]

None        no compression                         (40  MB  for f)
"JPEG"      lossy JPEG compression                 (FAILED  for f)
"LZW"       lossless LZW compression               (160 kB  for f)
"PackBits"  PackBits run-length encoding method    (1.5 MB  for f)
"ZIP"       lossless ZIP image data compression    (143 kB  for f)