How to add lines in TableForm

Using Graphics:

As suggested by Mr.Wizard in comments Graphics, inconvenient as it is, is way to get the desired output:

gF[txtopts_: {16, "Panel", Italic}, o_:{AspectRatio -> 1/GoldenRatio, ImageSize -> 500}] :=
   With[{d2 = Transpose@Reverse[Prepend[Transpose[Prepend[Transpose[#], #2]], 
    Prepend[#3, ""]]], dim = {1, 1} + Dimensions@#, prims = ##4}, 
    Graphics[{MapIndexed[Text[Style[#, ## & @@ txtopts], #2 - {.5, .5}] &, d2, {2}],
             Thick, Black, Line[{{0, Last@dim}, {#, #} &@Last[dim]}], 
             Line[{{1, First@dim}, {1, 0}}], prims}, Sequence @@ o]] &;

OP's example:

rowh = Table["C=" <> ToString[c], {c, 2, 10}];
colh = Table["K=" <> ToString[k], {k, 3, 10}];
redline = {{2, 9}, {2, 8}, {3, 8}, {3, 7}, {4, 7}, {4, 5}, {5, 5}, {5, 3}, {6, 3},
           {6, 1}, {7, 1}, {7, 0}};
blueline = {{2, 8}, {4, 8}, {4, 7}, {6, 7}, {6, 6}, {8, 6}, {8, 5}, {9, 5}};

gF[][m, rowh, colh, Red, Line[redline], Blue, Dashed, Line[blueline]]

Using Overlay:

ClearAll[itemF, mF, borderedF];
itemF[sides_: {{True, False}, {True, False}}, col_: Directive[Thick, Red]] := 
  Item[#, Frame -> sides, FrameStyle -> col] &;
mF = MapAt[itemF @@ #2[[1]], #1, #2[[2]]] &;
borderedF = Prepend[Transpose[Prepend[Transpose[#], #2]], Prepend[#3, ""]] &;


dat = borderedF[m, rowh, colh];
cells11 = {{4, 5}, {6, 6}, {8, 7}, {10, 8}};
cells12 = {{2, 3}, {3, 4}, {5, 5}, {7, 6}, {9, 7}};
cells21 = {{3, 3}, {4, 5}, {5, 7}, {6, 9}};
cells22 = {{3, 4}, {4, 6}, {5, 8}};
redborders = {{{{{True, False}, {False, False}}, Directive[Thick, Red]}, cells11},
              {{{{True, False}, {True, False}}, Directive[Thick, Red]}, cells12}};
blueborders ={{{{{False, False}, {False, True}}, Directive[Thick, Dashed, Blue]}, cells21},
             {{{{False, True}, {False, True}}, Directive[Thick, Dashed, Blue]}, cells22}};

opts = {ItemStyle -> Directive[16, "Panel", Italic], Spacings -> {1, 1}};

g0 = Grid[dat, Sequence @@ opts, Dividers -> {2 -> True, 2 -> True}];
g1 = Grid[Fold[mF, dat, redborders], Sequence @@ opts];
g2 = Grid[Fold[mF, dat, blueborders], Sequence @@ opts];

Overlay[{g1, g2, g0}, Alignment -> Center]

Here is my attempt. All the borders are correct except for the dual-coloured red line with blue dashes. It's a kludgy solution but shows possible techniques. In the following code I have left in Orange & Green to show some of the tricks. They can be switched to Black to reproduce the graphic. Grid is used.

m = {{3, 5, 5, 5, 5, 5, 5, 5}, {3, 6, 8, 8, 8, 8, 8, 8}, {3, 6, 10, 
    11, 11, 11, 11, 11}, {3, 6, 10, 14, 14, 14, 14, 14}, {3, 6, 10, 
    15, 17, 17, 17, 17}, {3, 6, 10, 15, 20, 20, 20, 20}, {3, 6, 10, 
    15, 21, 23, 23, 23}, {3, 6, 10, 15, 21, 26, 26, 26}, {3, 6, 10, 
    15, 21, 28, 29, 29}};

m = MapThread[
   Prepend, {Prepend[m, Table["K=" <> ToString[k], {k, 3, 10}]], 
    Prepend[Table["C=" <> ToString[c], {c, 2, 10}], ""]}];

(* Frame position: {Bottom, Left, Top, Right} *)

m[[1, 3]] = 
  Item[m[[1, 3]], Frame -> {False, False, False, False}, 
   FrameStyle -> Pink];
m[[1, 4]] = 
  Item[m[[1, 4]], Frame -> {False, False, False, False}, 
   FrameStyle -> Pink];

m[[2, 2]] = 
  Item[m[[2, 2]], Frame -> {False, True, True, True}, 
   FrameStyle -> None];
m[[2, 3]] = 
  Item[m[[2, 3]], Frame -> {True, True, True, False}, 
   FrameStyle -> Red];
m[[2, 4]] = 
  Item[m[[2, 4]], Frame -> {True, False, True, False}, 
   FrameStyle -> Directive[Blue, Dashed]];

m[[3, 1]] = 
  Item[m[[3, 1]], Frame -> {False, False, False, True}, 
   FrameStyle -> Orange];
m[[3, 2]] = 
  Item[m[[3, 2]], Frame -> {False, True, False, False}, 
   FrameStyle -> None];
m[[3, 3]] = 
  Item[m[[3, 3]], Frame -> {False, False, True, True}, 
   FrameStyle -> Red];
m[[3, 9]] = Item[m[[3, 9]], Frame -> False, FrameStyle -> None];

m[[3, 5]] = 
  Item[m[[3, 5]], Frame -> {True, True, False, False}, 
   FrameStyle -> Directive[Blue, Dashed]];
m[[3, 6]] = 
  Item[m[[3, 6]], Frame -> {True, False, False, False}, 
   FrameStyle -> Directive[Blue, Dashed]];

m[[4, 2]] = 
  Item[m[[4, 2]], Frame -> {False, True, False, False}, 
   FrameStyle -> None];
m[[4, 4]] = 
  Item[m[[4, 4]], Frame -> {False, False, True, True}, 
   FrameStyle -> Red];
m[[4, 7]] = 
  Item[m[[4, 7]], Frame -> {True, True, False, False}, 
   FrameStyle -> Directive[Blue, Dashed]];
m[[4, 8]] = 
  Item[m[[4, 8]], Frame -> {True, False, False, False}, 
   FrameStyle -> Directive[Blue, Dashed]];

m[[5, 2]] = 
  Item[m[[5, 2]], Frame -> {False, True, False, False}, 
   FrameStyle -> None];
m[[5, 4]] = 
  Item[m[[5, 4]], Frame -> {False, False, False, True}, 
   FrameStyle -> Red];
m[[5, 7]] = 
  Item[m[[5, 7]], Frame -> {False, False, True, False}, 
   FrameStyle -> Directive[Blue, Dashed]];
m[[5, 8]] = 
  Item[m[[5, 8]], Frame -> {False, False, True, True}, 
   FrameStyle -> Directive[Blue, Dashed]];

m[[6, 2]] = 
  Item[m[[6, 2]], Frame -> {False, True, False, False}, 
   FrameStyle -> None];
m[[6, 5]] = 
  Item[m[[6, 5]], Frame -> {False, False, True, True}, 
   FrameStyle -> Red];
m[[6, 9]] = 
  Item[m[[6, 9]], Frame -> {False, False, True, False}, 
   FrameStyle -> Directive[Blue, Dashed]];

m[[7, 2]] = 
  Item[m[[7, 2]], Frame -> {False, True, False, False}, 
   FrameStyle -> None];
m[[7, 6]] = 
  Item[m[[7, 6]], Frame -> {True, True, False, False}, 
   FrameStyle -> Red];

m[[8, 2]] = 
  Item[m[[8, 2]], Frame -> {False, True, False, False}, 
   FrameStyle -> None];
m[[8, 6]] = 
  Item[m[[8, 6]], Frame -> {False, False, True, True}, 
   FrameStyle -> Red];

m[[9, 2]] = 
  Item[m[[9, 2]], Frame -> {False, True, False, False}, 
   FrameStyle -> None];
m[[9, 7]] = 
  Item[m[[9, 7]], Frame -> {True, True, False, False}, 
   FrameStyle -> Red];

m[[10, 2]] = 
  Item[m[[10, 2]], Frame -> {False, True, False, False}, 
   FrameStyle -> None];
m[[10, 8]] = 
  Item[m[[10, 8]], Frame -> {False, True, False, False}, 
   FrameStyle -> Red];

Grid[m, Dividers -> {{2 -> Green, 3 -> Red}, {2 -> Green, 4 -> Red}}, 
 ItemSize -> 4]