Lambert is one of six candidates to succeed Martin Schulz, who is due to leave Parliament this month to return to German politics.
She said a Parliament under her leadership would "fight for human rights and democracy" and seek to improve transparency in the way the assembly works, including the activities of lobbyists.
Lambert, one of three women in the race, has little or no chance of victory, but said she was partly motivated to stand because there have been only two female Presidents since the first direct elections in 1979.
Speaking at a press briefing on Tuesday, she said, "I look at the photos of all the past Presidents and they are virtually all men. Gender balance is certainly something we need to look at."
Explaining her decision to stand, Lambert said, "We in the group looked at others standing and were not, frankly, very impressed and thought we could do just as well.
"If you look at Antonio Tajani, for instance, he is the epitome of the Brussels bubble - in other words, people who have been here for years. The bigger groups should not take the Greens and smaller groupings for granted. In selecting their candidates, none of them seem to have looked outside their own group and at the bigger picture. That is why we thought there should be an alternative."
She added, "Given that the UK is leaving the EU, the fact that I am British and standing for the presidency may have raised a few eyebrows, but the UK is still an EU member, an integral part of the Union, and still has a role to play. I consider it to be a great honour to be the Greens candidate.
"We live in a changing political landscape and both the EU and Parliament will have to assert themselves in order to maintain their position.
"I think Parliament and the EU could do more on this, for example, reasserting our position as a leader on climate change. Cutting our carbon footprint caused by meeting in Strasbourg would be one thing we could do.
"I have worked closely on the working time directive, but in many cases this does not seem to apply to many working here in the Parliament itself."
She refused to be drawn on what she might consider a successful performance in the election, adding that the group had yet to decide on who it would support if and when she drops out of the race.
She said, "It is a more open race than in the past and we will have to see what the other candidates have to say."
Lambert was, like many, taken aback by the Socialist decision to end the so-called grand coalition, the agreement with the EPP that would have seen a centre right member take the presidency for the second half of the legislature.
She said, "The EPP assumed this arrangement would continue but it has been ripped up by the Socialists and now everyone seems to be running around saying, 'Oh my God, what do we do?'"