LMX is quality of relationships between the leader and follower. As per socialexchange theory when a person provides something of value to another person, it becomes obligatory for the recipient to reciprocate (Blau, 1964), which yields beneficial consequences for the followers such as trust (Podsakoff, 1990, Childers, 2009), career advancement (Dubinsky et al., 1995), self efficacy (Walumbwa & Hartnell,2011), identification (Juan et al., 2011; Humphery, 2012) job satisfaction (Mohammad et al., 2011; Bushra et al, 2011; Yang et al, 2011) and job performance (Koh & Terbog, 1995; Geyer, 1998; Dvir et al, 2002). So, we have lot of literature which is delving upon positive outcomes of LMX. But in real life/work situations when two people have positive relationships, they also give undue advantages to each other e.g. a leader may recommend even undeserving follower for high post in the organisation due positive LMX. We need to interact on this issue.
One of the weaknesses is that the social exchange theory neglects culture context and variations of cultures. Meaning that the social exchange theory is based off a rewards concept, but all cultures are different and in some cultures they may not seek a reward for a relationship.
https://tcomm87.wordpress.com/social-exchange-theory/strengths-and-weaknesses-of-the-theory/
http://www.sociology.org/content/2005/tier2/SETheory.pdf
High LMX in some cultural contexts may cause avoiding constructive and open dialogue. In addition, it may hinder learning if learning oriented goals are not set, and instead individuals try to have impression management techniques to maintain or leverage their LMX via their performance goals. From SDT perspectives, it may be argued that the quality of relationships may have positive outcomes only when the positive and constructive values are internalized for forming the high LMX context.
There has been some research that I have seen presented at conferences (Southern Management Association, Eastern Management) but not in PRJ. When the focus is put on out-group members. These members increase negative extra-role behaviors. I would recommend looking at the online proceedings of those conferences.