Q:

Did Leopoldo Lopez take part in a coup against Hugo Chavez?

Leopoldo Lopez is currently in jail in Venezuela. He is considered to be a political opponent of Maduro, and his imprisonment is one of the main reasons why the 2018 Venezuelan elections were considered to be undemocratic, and thus why some nations refer to Maduro as a dictator rather than a president despite holding national elections.
I know that Lopez was arrested for alleged involvement in instigation of a riot, arson and violence in 2014, and that the case was highly dubious. But what I would like to know, is did he participate in the 2002 failed coup in Venezuela, and did he conspire with foreign governments during the failed coup attempt? 

A:

As a 2006 article in the LA Times states:

Though Lopez [...] says he didn't
  participate in the short-lived [2002] coup, he did help lead demonstrations
  against the fiery leftist president in the preceding days. He also was
  a driving force in the post-coup general strike that almost brought
  the Venezuelan economy to a halt.
[...]
Depending how the coup is perceived, Lopez either fully exercised his
  right to protest or crossed the line into insurrection by trying to
  bring down a democratically elected president.

A 2015 Foriegn Policy article further argues the case that López had an important if indirect role:

At the time of the coup attempt, the younger López, then 30, was mayor of Chacao, a Caracas subdivision. He supported both the general strike of April 9-10 and the massive opposition march on April 11 that immediately preceded Chávez’s removal. Both events were pivotal to the coup’s brief success, and López and Primero Justicia offered its leaders both legitimacy and a crucial base of popular support.

He is referred to there as "the younger Lopez" because his father was allegedly involved in a more direct way.
I'm not really seeing much in either article to imply or refute that he had foreign ties supporting him in any of this. 

A:

Kind of
He certainly arrested a Chavez minister. While he claims that he was just trying to keep them safe, I don't think even his supporters believe that: 

Many are still angry with him for taking part in the citizens arrest
  of Chavez's interior minister, Ramon Rodriguez Chacin, during the
  coup. And they say he has helped divide Venezuela by allowing his
  district's upscale Plaza Francia to become a base for dissident
  military officers and supporters of the post-coup strike.
Lopez distances himself from the coup organizers and says he refused
  to sign the decree by coup leader Pedro Carmona that in effect
  canceled Venezuela's Constitution. As for Chacin's arrest, Lopez
  insists that he and several of his police officers were invited by a
  neighboring mayor to take custody of the minister to protect him from
  an angry crowd that had surrounded the building where he was in
  hiding.
Dan Hellinger, a Venezuela expert and political science professor at
  Webster University in Missouri, called Lopez's claim that he acted to
  help the minister "disingenuous."

He also encouraged protests against the Chavez administration, but that's not really taking part in the coup in any sense.
Overall, it seems like he supported the coup, and took his chance when he could arrest a government minister. That last part in particular could be considered taking part in the coup. 
But haven't found evidence that he was a major player, or that he helped plan the coup ahead of time. Of course, I can't establish for certain that he didn't, either.  
As to whether he was "conspiring" with other countries, that's a tricky question. I can't find any direct evidence of it, but that doesn't mean it didn't happen. How probable is it?  
The main player to consider would be the United States. The government certainly knew that the coup was being planned: 

In a senior intelligence executive brief dated April 6 -- one of
  several documents obtained by Jeremy Bigwood, a freelance
  investigative reporter in Washington and posted on at
  www.venezuelafoia.info/, a pro- Chávez Web site -- the C.I.A. said
  that "disgruntled senior officers and a group of radical junior
  officers are stepping up efforts to organize a coup against President
  Chávez, possibly as early as this month." Those intelligence briefs
  are typically read by as many as 200 officials in the Bush
  administration.

However, the documents also suggest that the US wasn't a big fan of the coup, and didn't support it. 

The documents do not show that the United States backed the coup, as
  Mr. Chávez has charged. Instead, the documents show that American
  officials issued "repeated warnings that the United States will not
  support any extraconstitutional moves to oust Chávez."

Presumably this would have been out of pragmatic rather than ethical reasons, since the US government quickly recognized the government after Chavez was briefly overthrown.
That said, other sources have suggested the US did encourage the coup.

Reich is said by OAS sources to have had 'a number of meetings with
  Carmona and other leaders of the coup' over several months. The coup
  was discussed in some detail, right down to its timing and chances of
  success, which were deemed to be excellent.

This is, of course, also the position of various people close to the Chavez administration. 
Which source to believe?  I'm more incline to believe the first one, since it references leaked intelligence documents rather than anonymous sources. However, it's possible that they're both partially correct, and refer to the attitudes or actions of different individuals within the same administration. 
Regardless, one thing the two accounts concur on is that the US had some communication with the people planning to overthrow Chavez. It's possible that that included Lopez. But it's also entirely possible that it didn't. And, even if they did converse with him, if the first account is correct they might not have been too supportive. 

A side note. Obviously, the arrest of Lopez is a major factor in the perception of Maduro as a dictator. But I'm not sure it's the primary concern. As far as I can tell, two greater concerns are the disqualification of the major opposition parties for the 2018 election, and the attempted dissolution of the Asamblea Nacional and successful creation of a parallel constituent assembly. Additional concerns included historically low voter turnout, potential vote buying and voter bribery, and even direct vote tampering in the election, and restrictive press policies, targeting of dissenters, and rule by decree generally. 

