The Hammers entered in the first qualifying round by virtue of topping the Fair Play League and hold a 3-0 advantage from the first-leg.
A Diafra Sakho double in front of nearly 35,000 fans at the Boleyn Ground put the Hammers in command before James Tomkins wrapped up the simple victory with a second half header.
FC Lusitans have been knocked out in the first qualifying round of all of their four campaigns to date across the Europa and Champions Leagues.
New boss Slaven Bilic will once again be an on-looker as academy manager Terry Westley takes charge.
Birkirkara, of Malta, or Ulisses from Armenia await in round two. The pair drew 0-0 in the first leg.
The Hammers’ squad will yet again contain a mixture of senior and younger players, with a group of first teamers still on a training camp in Ireland.
Sakho should lead the line and fellow experienced squad member Joey O’Brien will make his 100th appearance for the Club.
Youngsters Josh Cullen, Reece Burke, Reece Oxford, Elliot Lee and Djair Parfitt-Williams will all hope for another opportunity after featuring last week.
West Ham can be backed at 1/33 to win in Andorra, winning you a cool £1 for every £33 staked. FC Lusitans showed little in the opening fixture to suggest they could pose a serious threat and their odds of 22/1 for victory mirror that. Those looking for a more backable price to play may want to delve into the 2/1 on Sakho to score first. He is a 1/5 poke to score anytime. Hammers youngster Oxford went close in the first-leg to scoring on his debut and his odds of 100/30 to net at any time looks a price to consider.