Article 17.2 of the UK/USA double tax treaty states that a lump-sum payment derived by a resident of one State from a pension scheme established in the other State shall be taxable only in that other State. This means that lump sums should only be taxed where the pension scheme is based i.e. UK scheme = tax free lump sum in UK.
Therefore, a UK National living in USA ‘should’ get lump sum payments that are tax free in UK should be tax free in USA. But this also depends upon which contracting state in the US they live in (remember the terminology is ‘contracting state’ and the USA is a union of ‘states’.
In addition, Article 1.4 states: “Notwithstanding any provision of this Convention except paragraph 5 of this Article, a Contracting State may tax its residents (as determined under Article 4 (Residence)), and by reason of citizenship may tax its citizens, as if this Convention had not come into effect” – i.e. each US state can simply ignore 17.2 but HMRC’s practice notes and tax manual (website) then states: “However, Article 1(4) will apply in respect of US citizens as the provisions of Article 17(2) are not amongst those listed at Article 1(5). So the US is able to tax lump sums received by US citizens from UK schemes and HMRC maintains that the provision preserves the exemption from income tax of a lump sum relevant benefit where it is paid by a UK approved pension scheme to a UK national beneficial owner who is a USA resident.
In short, for tax free lump sums from UK pensions schemes. USA citizens may face tax charges on any UK tax free sums received but UK citizens that are USA resident should still receive them tax free in UK and USA - but you may have to argue this point with both Federal Taxes and Local State Taxes.
Read HMRC tax manual: https://www.gov.uk/hmrc-internal-manuals/double-taxation-relief/dt19876a