Yes, I count my pension benefits in my net worth. No, you cannot just add in the lump sum value.
The reason is that pension benefits usually start at some date in future, not right now.
I do a net present value calculation. Basically I've figured out what the payments will be, assumed a SWR to get a future value that would support those payments, and then assumed an ROI on today's value to grow to that future value between now and when benefits would be paid. Invert and you can get today's value.
This calculation is very sensitive to the ratio of those two assumed values, so it's a rough guess at best. In my case, a federal pension of $5,331/yr paid out in 25 years is worth $31,053 today (about half of what has already been contributed). After one more year of work, it will pay $6,406/yr in 24 years and so is worth $39,555 today using the same assumed 4 percent SWR and 6 percent ROI.
These golden handcuffs are pretty strong in the case of federal pensions. In our case, the value of our pensions increases by more than our total salary if we work from age 57 to 58, because all of the big increases in pension value come at the very end of your working career. Retiring early just kills you on the pension.