Referee Michael Oliver booked Lewis-Skelly after the substitute trotted behind Raya's goal line while warming up in the 65th minute as the Gunners led 2-1.
Oliver observed the 17-year-old communicating with Raya before the Arsenal goalkeeper fell to the floor and stopped proceedings – as seen in new footage obtained by Mail Sport.
Lewis-Skelly had returned to the group of substitutes on the main touchline by the time he received his yellow card – handed out before he had played a single minute of professional football.
Mikel Arteta used the ensuing break in play to deliver a team talk to nine of his outfield players as they looked to keep City at bay. Pep Guardiola's side dramatically equalised in the 98th minute through John Stones and Arteta labelled his team's 10-man defensive effort as a 'miracle'.
Raya then went to the ground with an apparent injury, halting proceedings at the Etihad
In the build-up to Lewis-Skelly's intervention, Arsenal coaches had been motioning for calm in Raya's direction before he geared up to take a goal kick that was then ultimately delayed.
Gary Neville said 'there is no doubt that is a tactic' during commentary on Sky Sports when Raya went down to receive treatment.
The PGMOL confirmed that Lewis-Skelly's caution was for 'showing a lack of respect for the game' under the unsporting behaviour element of the laws. Arsenal have been approached for comment.
Apparent gamesmanship deployed by Arsenal was the talk of the top flight last year, with coaching staff and analysts across the division openly discussing the 'dark arts' among themselves. Clubs have sent concerns about the issue to the PGMOL.
Alleged delaying tactics are at odds with club legend Arsene Wenger's push to discourage time-wasting as part of his role as FIFA's chief of global football development.
Speaking last year amid a backlash against longer periods of stoppage time, Wenger claimed the new directives were to condition player behaviour.
'For the equity of the game, we want the team who wants to play to be rewarded,' he told the Independent. 'For the respect of the fan who sits in the stand, the teams to play, to encourage the teams not to waste time.'
The draw at the Etihad Stadium ended with nine yellow cards, including the pair handed to Leandro Trossard, with Erling Haaland furious at Arteta and Gabriel Jesus in the immediate aftermath of full time.
Haaland told Arteta to 'be humble' and had an expletive-laden exchange with Jesus.
Minutes before, a fired-up Haaland had thrown a ball at Gabriel's head in response to Stones' late goal. VAR reviewed the incident and deemed no action was necessary, with the Norwegian not facing any retrospective punishment.