Output resistance with no lambda SPICE parameter
The actual definition of \$g_{ds}\$ is

\$g_{ds} = \frac{\partial i_{ds}}{\partial v_{ds}}\$

The value of this mainly depends on both the model you use (changes with the "LEVEL" parameter for mosfet models) and the region the mosfet is used in (eg. triode or saturation).

For the LEVEL=1 model, the gds is calculated as

\$g_{ds} = \lambda\cdot\frac{\beta}{2}(v_{gs}-v_{TH})^2\$ in saturation

If you use this model, your formula (\$r_o=\frac{1}{\lambda I_D}\$) should match simulation results. If it is not the case, you should check that:


There are no other conductances connected to the node (eg. a load)
Check that the transistor is in saturation. The formula does not work for transistors in the triode region (linear region)
Unlikely the cause to your issue, but there are also conductances associated to the drain-bulk and source-bulk PN junctions.


For the LEVEL=2 model, \$\lambda\$ means something different. It will modify the current using:

\$I_{ds} = \frac{I_{ds}}{1-\lambda v_{ds}}\$

A default \$\lambda\$-parameter will be calculated if it is 0. Your formula will not work anymore for this model.

Although they're for HSpice, I found a nice reference for the main model equations per level here:

MOS Spice model equations and parameters

You can see that not even all models implement a "LAMBDA" parameter. For the ones that do, the LAMBDA parameter will do something else depending on the LEVEL-parameter.

For PSpice, I expect LEVEL 1 through 6 to be identical (they were implemented by the people from Berkeley themselves, who made the original Spice). The other mosfet model levels may differ a bit, although most models come back.

[EDIT]
To answer your second question:

For hand calculations, the one you're using is probably the most common one. It's just that you'll need to find \$\lambda\$ for your model and if you're using anything but a level 1 mosfet model, then the \$\lambda\$ you're looking for will not be the LAMBDA parameter of the model.

It may not be perfect, but it's enough for all practical applications.