This seems like a clear "take the lump sum" to me. Even if you stuck the money in a mattress, the pension @ $14,184/yr would take 13 years (until you're 73) to catch up to the 189k you'd get (after 92k tax free and paying 30% on 138k).
Tax Free Lump Sum: 92,918
Taxed Part of Lump Sum: 137,783
Taxes: 41,335
Net Lump Sum: 189,366
Pension of 1182/mo x 12 mo = 14184/yr. x 13 years = 184,392. Still less than the lump sum.
If you invested that lump sum starting at age 50 and got just 2% real return on it, the pension wouldn't catch up until you are age 87 (I'm using all real dollars, so that does account for the fact that you have a COLA inflation on the pension side of it). 3% real return and the pension doesn't catch up, ever.
Okay, so that's just the simple math. Now let's look at history, because we all know markets fluctuate.
So let's say you took that $189,366 today, at 50, invested it for a decade until 60, then started taking the SAME $14,184 you'd get from your pension (and adjust it upward for inflation each year, just like your pension does), and look at what happens.
Historically, after a decade, sometimes your money invested would be worth less, sometimes the same often more.
If you had done that plan, historically (using a 75/25 portfolio), 90.52% of the time you would not have run out of money. What that ("not run out of money") means in practical terms is you would have been able to supply yourself with that same inflation-adjusted pension you'd get anyways, starting at age 60, plus you'd have a big lump sum. In fact, the average ending portfolio would be $437,685 (median $363,333). The highest? $1,285,336. That's on top of taking out your pension every year, starting at age 60.
Of course, 10% of the time, you'd have had to cut back (or else ran out of money in that pension fund).
Whether or not that last 10% of stability is worth it is up to you, and depends on how conservative you are, but I personally would be looking at the fact that 90% of the time you can have your pension AND hundreds of thousands of dollars, and be going for that option.