I doubt whether it is in the best interests of the Trump administration to prosecute Lynch -- after all the conversation comes down to a he says, she says thing very little evidence. Now the admission from Comey (his own words) that he leaked information with evidence of what was leaked and to who - to back it up is a matter that is far more likely to have prosecution stick. But even then this is a weak case since the info Comey leaked was not classified, it was his own memo, and the question will be as the head of the FBI does Comey have the right to decide which non-confidential info to distribute to whom.
The Russia thing and the current hearings with Comey are a wet towel and only hurts the Democrats. If the Democrats want to remove Trump from office they would be far better off to focus on Trump' business interests and the ties to the administration. Hire a top tier law firm to investigate everything patiently for months, write a solid legal brief, do a court filing, and wait two weeks to build the media publicity then use the court action to demand that the Senate impeach the President if the case is solid. It may not be as "sexy" as shouting Russia, Comey firing, etc. but would be far more likely to stick as factual grounds for impeachment.
Drive enough of a wedge between the President and a few Republican Senator during the months leading up to the impeachment so several will come over and join the Democrats in voting "Yes". I can probably list at least a dozen Republican Senators (McCain, etc.) who would be likely to join because they already dislike Trump and if the evidence was solid they would gladly sign on for impeachment.
The Democrats need to create a strategic fact-based plan if they desire to take down the president with cause, and not focus on nonsense such as Russia, etc.