Both appeals are being heard in Wellington, with proceedings due to start today.
The case is expected to run for four days before Justices Anthony Randerson, John Wild, and Christine French.
At their sentencing last March, the Crown prosecutor, Colin Carruthers, QC, pushed for jail sentences of two to 2 years each for Graham, Jeffries and Bryant and two to two years nine months for Reeves.
The lack of remorse, absence of guilty pleas and limited reparation offers meant jail must be considered, he said.
Carruthers last Friday said he could not comment if he would push for a jail sentence during the appeal.
FMA chief executive Sean Hughes said the authority was not satisfied with the sentences imposed by Justice Robert Dobson last year but could not comment on the submissions in this week'sappeal.
The charges the former directors were found guilty of carry a maximum sentence of five years in jail or a fine of $300,000.
Although the Lombard directors had not intended to mislead, they had failed to disclose the company's deteriorating liquidity quickly enough, the judge said during sentencing.
When Graham was convicted on the charges last year, there were calls to strip the former director of his knighthood.
In an opinion piece last June, former minister of the Crown and Act Party leader Rodney Hide said: "If the conviction stands, John Key has a most unenviable task: he must ask the Queen to strip Sir Douglas of his knighthood."
The Lombard collapse, one of many finance company failures between 2007 and 2009, left 4400 investors owed $127 million.
"The majority are retired people who were critically reliant on getting their money back, if not the interest they anticipated earning," Justice Dobson said when sentencing the men last year.
"The crushing impact of the financial losses, and the emotional stresses caused by it, should not be underestimated."
The latest receivers' report says that investors have received 13c in the dollar so far.
According to the FMA, the value of investments and reinvestments made after the issuing of the offending offer documents in December 2007 was approximately $10.45 million.
During the eight-week trial of the four directors, evidence was given that Lombard sales staff were still soliciting members of the public to invest inMarch 2008, less than a month from the decision by the firm's trustees to call in receivers.