The command set logscale x will do the job.
set nokey
set title "Dynamical dominance criteria example"
set logscale x
set logscale y
set format y "10^{%T}"
plot "lambda.dat" using 1:2 lc 0 pt 12, \
"lambda.dat" using 3:($2*3):4 with labels
For me, the command set xrange [0.1:100] was not necessary, the range was chosen automatically. This is the result:

You did not provide your data, so I extracted it with g3data:
0.392 1.315e-13 0.392 Mercury
0.725 1.095e-11 0.595 Venus
0.994 9.520e-12 1.144 Earth
1.514 6.491e-14 1.514 Mars
0.994 1.216e-15 0.994 Luna
5.166 8.940e-08 5.166 Jupiter
9.543 4.136e-09 9.543 Saturn
19.24 3.286e-11 15.24 Uranus
30.35 1.843e-11 34.35 Neptune
39.48 1.946e-19 39.48 Pluto
2.797 1.183e-19 2.797 Ceres
40.18 6.960e-23 40.18 KBO
set logscale x?set xtics (0,1,10,100)and useset xr [0.1:100]; set logscale xinstead - that xtic at zero in combination with logscale looks suspicious...