Being a follower of the Giants drafts the last few years, you should have noticed that the only LBer we've picked above the 4th round was Clint Sintim in a year we had two second round picks (2009). He managed to play on and off for two seasons before entirely breaking down and hasn't seen the football field since 2010.
Now our man Reese tends to have a long memory and since then has taken the approach with respect to our LBing corps of throwing tons of able (but low draft priority and/or low end FA signings) bodies at the position and seeing what sticks. These include Herzlich, Greg Jones, Paysinger, Blackburn, JWill and most recently, Dan Connor.
LBer is the least prioritized position on the defense. As such, I don't anticipate the Giants picking one in the first round, especially when there is DL need as well (which is a priority for the Giants).
And I don't see a LBer in the first round that merits a change from that position with the possible exception of Arthur Brown which would be a total reach.
To whit ... Jameson Konz is exactly the type of low-key FA signing that Reese is known for and is not afraid to go into a new season with.