Here is an example in deciding lump sum as opposed to monthly payments.
The person has a choice of receiving a lump sum of $8,500 or a monthly payment of $77 for the rest of the life. This amount does not change, it stays the same for the life of the annuitant.
The person opts for monthly payment because the annuity calculations by insurance companies who back those annuities, would have required an investment of $12,500 to pay the same monthly amount of $77. In the mind of that person monthly payments were a better deal.
Of course there are assumptions involved, and certain amount of risk. It is longevity vs investment risk.
If the person lives for a long time, monthly payments will be worth it. If not, lump sum would have been better.
On the other hand if the lump sum is invested there are also certain risks involved. Will the initial investment generate money for the rest of the life of the investor? Or will the money dry up?
An additional consideration is diversification. You want to have different sources of income, giving you more stability, and peace of mind.