An era starts with the lead single and finishes whenever the tour comes to an end.

The Fame: April 2008-October 2009 (Just Dance-Bad Romance)
= 1 year, 6 months

The Fame Monster: November 2009-February 2011 (arguably May 2011, since the tour ended then)
= 1 year, 3 months

Born This Way: February 2011-February 2013 (Born This Way-end of tour).
= 2 years

ARTPOP: August 2013-November 2014 (Applause-end of tour)
= 1 year, 3 months

Longest = Born This Way, with 2 years.

Stripped

September 2002 - February 2004

HIStory: 2 years and 8 months
First single Scream in May 1995
Last single Smile in January 1998

JLos first 3 albums spent nearly a year each on the charts

JLo album charted in the UK in 2001,2002,2003,2004

I think it's GGGB/GGGB:R from 2007 to 2009 (the end of the GGGB tour)

I think Taylor her self-titled is her longest era so far. It was the 5th best selling album in 2008 and still in Top 40 in 2009 despite been released in 2006

Screaming that the fame monster had a longer era than ARTPOP

No Gaga stans has done it as asked in the OP (And I get why cuz Billboard is a ****** website) but I'll give it a go

The Fame: August 2008 - March 2010
The Fame Monster: October 2009 - September 2010
Born This Way: February 2011 - February 2012
ARTPOP: August 2013 - April 2014

The Fame was the longest, 1,5 years Paparazzi stayed strong through Bad Romance and the beginning of Telephone

WUIV, its longevity

No tours allowed