As Terrell noted, the Lazor firing is to be expected, as Taylor would presumably hire his own coaches.
Lazor was hired by former Bengals head coach Marvin Lewis to be the team's quarterbacks coach in 2016. He took over as offensive coordinator for the fired Ken Zampese during the 2017 season.
Lazor's 2017 season was somewhat encouraging, as a team that scored just nine points in their first two games managed 20 or more in eight of their next 10 under the new offensive coordinator's watch. But an ugly two-game stretch in December that saw the Bengals get outscored 67-14 ended their playoff hopes.
The Bengals got off to a hot start in 2018 thanks to 31.5 points per game in their first four outings, and the team was in first place after five weeks with a 4-1 record.
However, they took a giant step back in blowout losses to the Kansas City Chiefs and the New Orleans Saints before starting quarterback Andy Dalton and wideout A.J. Green were lost for the season with injuries.
The Bengals scored more than 21 points just one time in their last seven games en route to a 6-10 finish. Still, Lazor doesn't shoulder the primary blame for the team missing the playoffs: The Cincinnati defense was arguably the No. 1 reason, with the team allowing the third-most points in the league.
Coincidentally, Taylor replaced Lazor as the Miami Dolphins' offensive coordinator in 2015 when the latter was fired following the team's 4-7 start. Miami finished No. 27 in scoring, although the Dolphins offense was eighth in Football Outsiders offensive DVOA (defense-adjusted value over average) the season before.
As Terrell noted, however, it's "definitely a new era in Cincinnati," as Taylor would take over for Lewis, who had been with the Bengals since 2003.
This would be the 35-year-old Taylor's first head coaching gig.