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There are countless times in which a player became a well-established veteran during his time as a BC Lion, but then because of free agency or trade, he went to another CFL team and he continued to show his great performance with his new team(s). Excellent examples by position are:
Quarterback: Doug Flutie and Matt Dunigan
After winning 1991 MOP, Flutie had four great seasons as a Stampeder with three MOP's and then two more great GC and MOP seasons as an Argonaut. For Dunigan, he had two-injury but still good seasons as an Argonaut, then had great seasons with a Blue Bomber and established a record of 713 yards passed.
Running Back: Andrew Harris
After leaving the Lions for Winnipeg in 2016, he won MOC in 2017 and all-star selections in each season.
Receivers: Jason Clermont, Geroy Simon, and David Williams
Clermont and Simon continued to have decent seasons as a Roughrider, and recent inductee Williams continued to connect well with Dunigan in both Toronto and then Winnipeg.
Defensive Players: Alondra Johnson and Willie Pless
After good performance as a Lion in 1990, they bolted to Alberta teams where they continued to have several great all-star performances.
I won't be surprised at all if Solomon Elimimian will be added to the last list.
If a person does very well for a particular team and wins individual awards, all-star selections, and other accolades, one is immediately held to the highest standards and expectations especially if they join another team. Let's see of historical good veterans who were the signed by the Lions.
What I consider to be GOOD veterans are those who did very well with their previous team, and then continued to do very well as a BC Lion.
And what I consider to be BAD veterans are those who did very well with their previous team and thus were held to very high standards and expectations, but then were considered a huge disappointment in that they didn't fulfill their expectations.
Here's my list. And as usual, I may use pairs if I think their situations are similar.
GOOD established Veterans who did well when they joined the BC Lions 
1. Wally Buono and Don Matthews
The first has to be not coaches but players. Buono became a legendary head coach when he coached the Stampeders starting in 1990. He did just as well when he joined the Lions in 2003.
Don Matthews was an assistant coach as part of the Eskimo dynasty from 1978-82, and made an immediate impact when he became HC in 1983 for the Lions.
2. Paul McCallum
Despite his huge choke in the 2004 WDF, McCallum had the starting placekicker for over a decade in Saskatchewan. The Lions gave him a chance in 2006 and worked well with GC MVC and Special teams awards.
3. Kent Austin and Danny McManus
Kent Austin was an established good veteran who passed over 6,200 yards in 1992 as a Roughrider and my personal bias, I stated countless times he was an excellent replacement over Danny Barrett. Danny McManus was a solid backup as a Blue Bomber, and continued that in 1994.
4. Matt Dunigan and Damon Allen
Both QB's started their careers in Edmonton where they proven themselves as excellent quarterbacks. They performed well during their times as a Lion. For Allen despite the fact that most fans were frustrated with him, no doubt he also performed well for the Lions too.
5. Dave Dickenson
He was 2000 MOP as a Stampeder, and most Lions fans like him during his time in BC. He was 2003 MOP and 2006 GC MVP.
6. Less Browne and James Jefferson
Two good former defensive players who did well for Winnipeg in were part of the integral 1994 Lions teams.
7. Jimmy Cunningham + Arland Bruce III
Both players may be better remembered as Argonauts, but were an integral part of the 2000 and 2011 Lions GC teams respectively.
8. Robert Drummond and Chris Perez
Drummond won three straight GC as a Stallion and then Argonaut, and then won the 2000 GC along with Chris Perez.
9. Jan Carinci
Caught a TD for the Argonauts in the 1983 GC, and then became a solid receiver for the Lions.
10. James "Quick" Parker"
Good established defensive player for the Eskimos who then did well as a Lion by winning a pair of defensive player of the year awards.
BAD established Veterans who did well when they joined the BC Lions 
1. Danny Barrett
Led the Stampeders in a 1991 GC appearance, was brought in to replace Doug Flutie. Failed big time.
2. Charles Roberts
Long time running back in Winnipeg. Survived just on season in BC.
3. Stewart Hill and Chris Skinner
Did well as an Eskimo, but not so as Lions.
4. Mark Gastineau
Best example for an ex-NFL player. Won several all-star selections as a NY Jets. Played just 4 seasons as a Lion in 1990 before he was released.
5. Robert Mimbs
1991 MOP runner-up. Didn't do well when he became a Lion in 1992-93, but did better when he moved on to Saskatchewan.
6. Brett "the Toaster" Williams
Good defensive player in Montreal, but just played on season as a Lion.
7. Kevin Glenn
Won awards in other teams, but played just one year in 2014 and was not re-signed.
8. Emanuel Tolbert
Received from the Dunigan trade. Did well for the Argonauts, but not as a Lion.
9. Gilbert Renfroe
Led the Argonauts to the 1987 GC appearance and 1988 14-4 record. Wasn't much help when he joined the Lions in 1992.
10. Bob O'Billovich
Did fairly well as HC in Toronto, but in 1992 after Doug Flutie left, his team went 3-15 and was fired.