One of those was last weekend's 3-1 win over West Ham as the Gunners picked up their first points of the campaign.
Mesut Özil is back in contention for a place in the Arsenal starting lineup at Cardiff but the challenge of adapting to the needs of his new manager remains.
The Gunners led twice, through Shkodran Mustafi's header and a curling effort from Pierre-Emerick Aubameyang, before Lacazette crashed home the victor on 81 minutes.
Giggs will be in Cardiff for the Premier League match as he prepares for Uefa Nations League games against the Republic of Ireland and Denmark on 6 September and 9 September respectively.
But Cardiff responded again, this time eight minutes later, when Sean Morrison nodded Joe Ralls' free kick back across goal to Danny Ward, who headed home off the left post. That subsided and the game settled into a pattern of Arsenal dominance. The France global also set up Pierre-Emerick Aubameyang to make it 2-1 in the 62nd, making a strong argument for why the two forwards should be starting together regularly.
He drifted out of the game as it progressed but started well.
Chief among the Emery;s concerns was the continued struggles of goalkeeper Petr Cech to deal with the Spanish manager's commitment to build from the back.
Sunday's encounter was a game most would have expected Cardiff to lose but they will rue the result as an opportunity lost after almost snatching a valuable point.
For all the talk of Emery needing "three or four transfer windows" to make this Arsenal team his own, winning the majority of this type of fixture looks an attainable short-term target. They know that they will be in selection in the next game, even if they did not play well this time. The fact that they netted twice could be seen as a comfort, but it's also worrying that they couldn't turn that into at least a draw.