The Croat defeated the Serbian in straight sets 6-3, 6-2 securing a spot in the quarter-finals.
On Tuesday, the 24-year-old rallied past Botic van de Zandschulp - who enter the tournament with a wild card, beating the Dutch in two sets 6-4, 7-6 (4).
On Thursday, a top performance allowed Coric to move past Lajovic; he will now face Kei Nishikori on Centre Court, Friday.
Nishikori, 31, overcame Felix Auger-Aliassime - earning his first victory in five months, and Alex de Minaur, showing he is back on tour and ready to fight.
The Japanese underwent surgery on his right elbow in October 2019; in 2020, he contracted COVID-19 and suffered another injury to his shoulder while playing the second round of Roland Garros.
“I don’t feel 100 percent yet, but I think its on the way,” he said to ATP Media.
LAJOVIC CAMPAIGN IN ROTTERDAM
The Serbian defeated Medvedev at the Rotterdam Ahoy in straight sets 7-6 (4), 6-4, disrupting the Russian chances to a Top-2 breakthrough had he reached the tournament finals.
The 25-year-old began the season in exceptional form, helping his country capture the ATP Cup in Melbourne, to then reach the Australian Open finals - which he lost to world No. 1 Novak Djokovic, breaking the Russian streak of winning 20 of his past 21 matches.
An erratic Medvedev produced 25 unforced errors and eight double faults against Lajovic, 30, who remained in the game, focussed at all times, even when he experienced an early break during the first set.
Before the event started, only 115 points separated the Russian from World No. 2 Rafael Nadal, who withdrew from the tournament due to a back injury.
With the Russian loss, the Spaniard maintains his place in the rankings.
Wins and Losses
Former champions Stanislas Wawrinka and Andy Murray said farewell to Rotterdam.
Wawrinka, 35, who won the event in 2015, fell to Karen Khachanov on Tuesday; the Russian claimed the win over the Swiss 6-4, 7-5 in one hour and 32 minutes.
Murray, 33, received a wild card to play in Rotterdam; he conquered his first win of the year, overcoming Robin Haase 2-6 7-6 (2) 6-3.
On Wednesday evening, the 2009 champion played fourth seed Andrey Rublev, who outlasted the Briton with a 7-5, 6-2 victory.
Third seed Alexander Zverev played against 23-year-old Alexander Bublik in the first round, going down in straights sets 5-7, 3-6.
Contesting the second round on Thursday, Bublik lost to Tommy Paul 7(5)-6, 3-6, 1-6; the American will face Marton Fucsovics.
The qualifier earned the last spot in the quarter-finals defeating Spaniard Alejandro Davidovich Fokina in straight sets 6-3, 6-2.
Fokina sent home early, countryman Roberto Bautista Agut with a 6-2, 7-6 (3) triumph.
Also, the 2021 Open Sud de France champion, David Goffin, met French qualifier Jeremy Chardy on Thursday, with the latter prevailing over the sixth seed 7-6 (3), 7-6 (5) in one hour and 44 minutes.
Chardy, 34, will face world No. 8 Rublev, while Stefanos Tsitsipas will meet world No. 21 Khachanov.
The 22-year-old battled against Egor Gerasimov and Hubert Hurkacz, reaching the last eight.
The quarter-finals will be played on Friday.
The 48th ABN AMRO World Tennis Tournament is held from 1 until 7 March, without spectators due to the ongoing Covid-19 pandemic.