The bank said at the third quarter that non-core assets had fallen to £70 billion from £200bn at end-2010, and it expected that figure to come down to about £66bn by the end of 2013.
City analysts said Lloyds chief executive Antonio Horta-Osorio was likely to face questions about how much, if any, of the remaining non-core business might be switched back into core operations ahead of a sale of more government shares in the bank later this year.
One said: “The progress Lloyds has made in running down the non-core assets means we are now fast approaching the rump of what is left.
“Usually when you get down to that point decisions have to be made on what of the non-core might now have improved trading to the extent that you may want to switch them back into the core franchise. It is an area of interest for the City.”
The bank has sold fund manager Scottish Widows Investment Partnership, its German life insurance business, and some US mortgage-backed securities and Irish retail mortgages.
However, Lloyds still has some retail operations in the Republic of Ireland and Horta-Osorio is likely to be quizzed on whether he wants a complete Irish exit or not.
The reduction in non-core assets was a big factor in a 44 per cent fall in bad debts at the bank in the first nine months of 2013, and that trend is likely to have continued in the fourth quarter.
In a trading update last week, the bank said it expected to report an underlying profit of £6.2bn for 2013.
Lloyds also said it expected to return to a small statutory headline profit in 2013. City analysts believe this will be in the region of £200 million.