Lewis-Francis finished fourth in his heat in 10.39 seconds while Aikines-Aryeetey was second in his – behind favourite Christophe Lemaitre of France - running 10.27.
Britons Luke Lennon-Ford and Richard Buck were disqualified after winning their 400m heats in Finland for running out of lane.
Goldie Sayers topped her javelin qualification group, throwing 60.90 – one of only two athletes to achieve the 60m automatic qualification.
Nathan Woodward, Meghan Beesley (both 400 hurdles), Ashlee Nelson (100m) and Mukhtar Mohammed (800m) also progressed in their respective events.
Later on Wednesday, British favourite Mo Farah contests the only event to be decided on the opening day, the 5000m.