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You’ll have to read the plan documents to get an answer as the specific rules will be in there. You also should check on tax implications. Some lump sum amounts can be rolled into an existing IRA or 401(k) and some cannot (and are immediately taxed as wage income).
Also worth looking at is what happens to the annual payments if you die. In some plans they stop, some have a reduced benefit for a spouse, and some are inherited by the spouse with no reduction. This could be a big factor in taking the lump sum versus the annuity, especially if you have poor health or engage in risky fun.
And to your question on whether the lump sum is bigger when interest rates are lower, that is generally true but again the specifics will be in your plan documents. Most plans are required to make these documents available to any participant that requests them. You may need professional advice to understand them and evaluate your options.
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