Hi John,
If your ESA is entirely contributory (with no income related top-up) then DWP will not need to be informed about any lump sum.
The situation is different for regular pension payments. The first £85 per week will be discounted, then your ESA would be reduced by £1 for every £2 of pension. You should notify DWP even if weekly payments are less than £85 as not doing so can cause problems further down the line.
Nothing on this board constitutes legal advice - always consult a professional about specific problems