Hi!
Lamda is the process parameter and it is not any design parameter that u have mentioned. For process parameter I feel u have to give look to the semiconductor processes and the BSIM manual were it will be mentioned how lamda is calulated.
In BSIM no straight formula for lambda exist because it depnds on many different parameters. but for your hand calculations you can simulate a simple ckt (as CS) and then from the output paramters of spice make an approximation about lambda: Id=K/2* (Vgs-Vt)^2*(1+lambda*Vds)
Lamda is not fix value for the transistor. It is varies for different biasing and different model of transistor. you can find it by drawing the Id-Vds curve and find the gradient At the specific biasing you want at the curve. The gradient is lamda value. that is what i know.
Lambda varies with process ,device parameters and more. simualte simple fet Id ,Vds char and extend the I line to - axis of Vds ,the point it cuts gives u 1/Lamda.
Or if u have Gds of ur fet ,then Lamda=Gds/Id
Note that its different for diff. values of Id also
As it is known, λ is fixed for a give value of W/L, Vgs, Vds. Thus, for a given transistor, fix all these for the MOS to work in the saturation region and run a DC Operating Point simulation.
Look into the values of rds of the MOS and the Ids thro' it.
Calculate λ using the following relation: