Inter were three goals up in the 28th minute as Lukaku bagged his second after Roberto Gagliardini had smashed in a volley.
The transfer window closes on October 5 and Koeman admitted he would like to see another central defender arrive before then.
"I'm really pleased with the victory. It's always tough to start the tournament. I was a bit nervous. She played really well in the first set, she didn't miss. Then I just found the rhythm," said the 2018 champion.
Jepkosgei will return to the same course she shattered the world record in 2017 in half marathon and will face up against fellow countrywoman Joan Chelimo.
Patrick Bamford became the first Leeds United player to score in each of the first three matches of a season as his 88th minute header gave his side all three points from their short trip to play Sheffield United.
The 16 teams were divided into two groups this season, with the top four teams in each group moving into Final A for the championship race while the bottom four falling into Final B for the 9th to the 16th places.
MEXICO CITY, Oct. 1 (Xinhua) -- Wolverhampton Wanderers forward Raul Jimenez was Thursday among 11 Europe-based players named in Mexico's squad for friendlies against the Netherlands and Algeria.
Real Sociedad ruined Elche's return to the top flight as they won 3-0 in Elche's Martin Valero stadium with second half goals from Portu, Adnan Januzaj and Roberto Lopez.
Tao Guannan from Guangdong and Shandong's Liu Zongyu took second and third places respectively.
Last-placed Dijon was closed to clinching its first win of the news season, but an injury-time penalty from Teji Savanier crashed their hopes as the team was held to a 2-2 draw at home against Montpellier. Enditem
The 39-year-old tennis great, who is seeking a record-equaling 24th Grand Slam title, skipped all the tune-up tournaments for the clay major and practised at the Mouratoglou Academy, but acknowledged she was "not one hundred percent" as the French Open started.