Clear[Kc, vc, Ks, vs, y, Db, s, lam, l, solution, f, upperl]
upperl = 135;
Kc0 = 1.9;
y0 = 0.47;
y2Ks[yy_] := 
        Sqrt[(1 + 0.5*yy)/(1 - 0.5*yy)];
y2vs[yy_] := Sqrt[1 - 0.25*yy^2];
r1[KKc_, vvc_, vvs_] := (vvs/vvc)^(2 - KKc);
r2[KKc_, vvc_, vvs_] := (vvs/vvc)^(-KKc);
r3[KK_] := 1 + (1/KK^2);
r4[KK_] := 1 - (1/KK^2);
f[KKc_, vvc_, KKs_, 
          vvs_] = -0.25*(r1[KKc, vvc, vvs]*r4[KKc]*KKc + 
              r2[KKc, vvc, vvs]*r4[KKs]*KKs);
\(\(solution = 
        NDSolve[{
\(Kc'\)[
                l] == \(-0.5\)*\((vc[l]/vs[l])\)*\((Kc[l]^2)\)*
                Db[l]*\((1 - \((2/3)\)*r1[Kc[l], vc[l], vs[l]]*
                      r3[Kc[l]]*\((2.75 - Kc[l] - Ks[l] - 
                          y[l])\))\), 
\(vc'\)[
                l] == \(-0.5\)*\((Kc[l]/vs[l])\)*\((vc[l]^2)\)*
                Db[l]*\((1 + \((2/3)\)*r1[Kc[l], vc[l], vs[l]]*
                      r4[Kc[l]]*\((2.75 - Kc[l] - Ks[l] - 
                          y[l])\))\), 
\(Ks'\)[
                l] == \(-0.5\)*
                Ks[l]^2*\((y[l]^2 + 
                    Db[l]*\((1 - \((2/3)\)*
                            r2[Kc[l], vc[l], 
                              vs[l]]*\((r3[
                                    Ks[l]]*\((2.75 - Kc[l] - Ks[l] - 
                                      y[l])\) + 
                                4*y[l])\))\))\), 
\(vs'\)[
                l] == \(-0.5\)*Ks[l]*vs[l]*
                Db[l]*\((1 + \((2/3)\)*r1[Kc[l], vc[l], vs[l]]*
                      r4[Ks[l]]*\((2.75 - Kc[l] - Ks[l] - y[l])\))\), \(y'\)[
                l] == \((2 - 2*Ks[l])\)*y[l] - 
                Db[l]*\((1 - 
                      r2[Kc[l], vc[l], 
                          vs[l]]*\((1 + \((1/3)\)*r4[Ks[l]]*y[l]*
                              Ks[l]*\((2.75 - Kc[l] - Ks[l] - y[l])\) + \((2/
                                  3)\)*r3[Ks[l]]*y[l]*
                              Ks[l]^2 - \((4/3)\)*\((Kc[l] - Ks[l] + 
                                  y[l])\))\))\), 
\(Db'\)[
                l] == \((2.75 - Kc[l] - Ks[l] - y[l])\)*Db[l], \(s'\)[
                l] == \(-s[l]\) + 
                s[l]*Sqrt[s[l]]*
                  Db[l]*\((\((1 - 
                          f[Kc[l], vc[l], Ks[l], vs[l]])\) + \((4/7)\)*
                        f[Kc[l], vc[l], Ks[l], 
                          vs[l]]*\((2 - Kc[l] - Ks[l] - y[l])\)*\((1 - 
                            Exp[\(-7\)*
                                l/4])\))\), 
\(lam'\)[
                l] == \(-lam[l]\)*Sqrt[s[l]]*
                Db[l]*\((\((1 - f[Kc[l], vc[l], Ks[l], vs[l]])\) + \((4/7)\)*
                      f[Kc[l], vc[l], Ks[l], 
                        vs[l]]*\((2 - Kc[l] - Ks[l] - y[l])\)*\((1 - 
                          Exp[\(-7\)*l/4])\))\), 
Kc[
                0] == Kc0, 
vc[0] == 
              1.0, 
Ks[0] == 
              y2Ks[y0], 
vs[0] == 
              y2vs[y0], 
y[0] == 
              y0, 
\ 
            Db[0] == 0.025, 
\ \ s[0] == 
              5, 
\ lam[0] == 1}, {Kc, vc, Ks, vs, y, Db, 
            s, lam}, {l, 0, upperl}];\)
\)
ParametricPlot[Evaluate[{Kc[l], Db[l]} /. solution], {l, 0, upperl}, 
      PlotRange -> All, ImageSize -> 600]
  
Plot[Evaluate[{Kc[l]} /. solution], {l, 0, upperl}, 
      PlotRange -> All]
Plot[Evaluate[{Db[l]} /. solution], {l, 0, upperl}, 
      PlotRange -> All]
Plot[Evaluate[{y[l]} /. solution], {l, 0, upperl}, 
      PlotRange -> All]