Is there any consensus of what caused the Lusi Mud Volcano eruptions in Indonesia?
No, there is no consensus.

In fact, there's quite a bit of debate about it — around the 2 causes you mentioned. To sum up the proposed triggers:


The eruption happened about 2 days after the 2006 Yogyakarta earthquake, which killed over 5000 people. Lupi et al (2013), Sawolo et al. (2011), and others including the Indonesian government, favour this as the trigger. 
The eruption happened about 200 m away from Lapindo Brantas's Banjar Panji 1 exploration well. There were early signs of trouble in the well, which started when the earthquake happened. At the time, the incident was treated as a blow-out, relief wells were drilled, etc. Davies et al. (2011), and others, blame this. 


Last year I blogged about Lusi. The first-order cause was not my focus (though I insinuated that I thought the well exploited a predisposition set up by the earthquake); I focused instead on the history of the event. But much of the controversy emerged in the comments, which are worth reading. 

Rather than trying to synthesize everything into an elegant summary, I'll just point out two of the complications in all this:


The Lupi et al (2013) argument has serious flaws, because the authors misinterpreted the sonic (DT) log from the well. This was partly, but not completely, resolved by the corrigendum published in 2014. In a nutshell, the fast layer they argued for was a logging artifact.
There is a legal backdrop to the argument, which may not be compatible with an objective scientific debate. For the company, there is the question of liability and thus reparations, which could be expensive. For the government, there is the question of international financial relief, some of which is contingent on Lusi being a natural disaster. 


The debate may not be satisfactorily resolved for some time. It seems to be one of those unhelpful debates where, to the participants at least, there is no uncertainty. My heuristic in such situations is to assume this means that "it's complicated".

References


Davies, R, S Mathias, R Swarbrick and M Tingay (2011). Probabilistic longevity estimate for the LUSI mud volcano, East Java. Journal of the Geological Society 168, 517–523. DOI 10.1144/0016-76492010-129.
Lupi, M, EH Saenger, F Fuchs and SA Miller (2013). Lusi mud eruption triggered by geometric focusing of seismic waves. Nature Geoscience 6, 642–646 (2013) DOI 10.1038/ngeo1884.
Sawolo, N, E Sutriono, B Istadi, A Darmoyo (2009). The LUSI mud volcano triggering controversy: was it caused by drilling? Marine &amp; Petroleum Geology 26 (9), 1766–1784. DOI 10.1016/j.marpetgeo.2009.04.002.