Morrison took to social networking site Twitter to give an update after Lazio's latest pre-season match on Wednesday.
And he revealed he had scored another two goals to add to the brace he got in his first game at the weekend.
He said: "Game two finished another win and another two goals."
'The best talent since Paul Scholes'
The former Manchester United midfielder, who was once hailed the Red Devils' best talent since Paul Scholes by none other than Sir Alex Ferguson, was released by the Hammers last season.
The immensely talented star, likened by some West Ham fans to their legendary midfielder Sir Trevor Brooking for the way he effortlessly glided past opponents, looked to have got his career back on track in East London.
He had been disposed of by a frustrated Sir Alex and West Ham co-owners David Sullivan and David Gold took a punt on the England youth international.
It looked to have paid off when, after a spell out on loan, Morrison forced his way into Sam Allardyce's side and started scoring goals - most memorably away to fierce rivals Tottenham Hotspur in a 3-0 Premier League win.
West Ham glory did not last long
But it soon turned sour as Morrison's infamous lack of discipline saw him fall out of favour yet again.
After a series of loan spells at Queens Park Rangers and Cardiff, the Hammers eventually gave up on the 22-year-old and terminated his contract in February, freeing him up to join Serie A side Lazio.
Initial reports by the likes of the Mirror suggested he was homesick and wanted to return to England before a ball had even been kicked in anger in Italy.
Has the penny finally dropped?
But he seems to have knuckled down and after impressing on his debut with two goals in a 14-0 win last week, he has now followed it up with another brace.
The opposition clearly were not up to much this time either as Lazio ran out 9-1 winners over Top 11 Radio Club.
But his form and new-found focus will be concerning for West Ham and the club's fans, many of whom wanted to see how the prodigious talent fared under a different manager than Allardyce.
They now have that in the shape of Slaven Bilic who has been brought in partly for his more attack-minded philosophy.
But Bilic also demands a high work rate from his players, something Allardyce accused Morrison of lacking when he excluded him from his team after his initial breakthrough.
The Pogba problem
It remains to be seen whether Morrison will stay the course over in the Italian capital, having pushed West Ham's patience to the limit during his time at the club.
But like his old Manchester United youth teammate Paul Pogba has shown with Juventus, should he excel it could prove a lack of patience which ultimately costs the club one of the most exciting young players in Europe.