Designing a MOSFET current mirror circuit
\$r_o&gt;5\rm{k\Omega}\$ is the condition that sets the length of the transistors. It is desired for the PMOS current source and the NMOS current sink to have an output impedance \$r_o\geq 5\rm{k\Omega}\$. Knowing that \$I_D\$ is 50 or 100μA,
$$\frac{\Delta V_{DS}}{\Delta I_D} = r_o = \frac{1}{\lambda I_D}$$
Thus, for the PMOS,
$$\lambda = \frac{1}{r_oI_D}\leq \frac{1}{5\rm{k\Omega}\times50\rm{μA}}=4\rm{V^{-1}}$$
Likewise, for the NMOS, \$\lambda \leq 2\rm{V^{-1}}\$.

For a given device type, \$\lambda\$ is dependent only on \$L\$ and does not depend on \$W\$ or \$I_D\$. Therefore, this is the sequence of steps you should follow:


Determine what values for \$L\$ will give the desired \$\lambda\leq2\rm{V^{-1}}\$ for NMOS and \$\lambda\leq4\rm{V^{-1}}\$ for PMOS. Use the simulator to help. Generally, \$\lambda\$ scales inversely with \$L\$.
With the target value of \$V_{OV}=0.3\rm{V}\$, calculate the required \$W\$.
You already know that \$R=8\rm{k\Omega}\$.
You already know to scale the PMOS by \$2\times\$ and NMOS by \$4\times\$.