There is no guarantee that the three curves will intersect, but you may be able to compute parameters that make them intersect.
In any case, here is an example with curves.
\[Alpha] = 1; m = 2; \[Lambda] = 0.2; \[Mu] = Log[2]/120;
p1 = ParametricPlot3D[{(\[Lambda]/\[Mu]*u^m)/(1 + u^m),
u, (\[Lambda]/\[Alpha]*u^(m - 1)/(1 + u^m) - \[Mu]/\[Alpha])}, {u,
1, 10}, PlotRange -> {{0, 100}, {1, 10}, {0, .5}}, BoxRatios -> 1,
PlotStyle -> {Blue, Thickness[0.01]}]
p2 = ParametricPlot3D[{(\[Lambda]/\[Mu]*u^m)/(1 + u^m),
1, (\[Lambda]/\[Alpha]*u^(m - 1)/(1 + u^m) - \[Mu]/\[Alpha])}, {u,
1, 10}, BoxRatios -> 1, PlotStyle -> {Red, Thickness[0.01]},
BoxRatios -> 1]
p3 = ParametricPlot3D[{(\[Lambda]/\[Mu]*u^m)/(1 + u),
1, (\[Lambda]/\[Alpha]*u^(m - 1)/(1 + u^m) - \[Mu]/\[Alpha])}, {u,
1, 10}, BoxRatios -> 1, PlotStyle -> {Green, Thickness[0.01]},
BoxRatios -> 1]
Show[p1, p2, p3]