Important:
This answer is based on tax law for the tax year ending 28 February 2020.
Answer:
We are not sure why you believe there will be ‘a conflict’, as you say. From a tax point of view there would be none.
In fact, it is common for a severance benefit and a lump sum benefit to accrue in the same year of assessment.
Because you say that the individual is entitled to take “one third of his pension” (we accept this is one third of the retirement interest), we accepted that the person actually retires. You will need to confirm this. In other words, it is not a withdrawal benefit (taken before normal retirement age).
The two lump sum amounts are then taxed according to two different tables. The rates of tax, and the amount at which the 0% applies, are the same in both these tables. Because both, all three of them actually, applies to the cumulative lump sums, the R500 000 is only available once. It matters not, in what order the lump sums accrue.