Two severe cyclones connected by a monsoonal trough
Let us state the obvious reasons first:


Warm SSTs along the Timor Sea as well along the Queensland coast favour the formation of Tropical Cyclones - 

The following two URLs show the SSTs along the Northern as well as Eastern Coast of Australia for the referenced periods. 
a) http://earth.nullschool.net/#2015/02/15/2100Z/ocean/primary/waves/overlay=sea_surface_temp/orthographic=136.27,-24.99,512

b) http://earth.nullschool.net/#2015/02/20/2100Z/ocean/primary/waves/overlay=sea_surface_temp/orthographic=136.27,-24.99,512

The threshold SST required for tropical cyclogenesis is 26.5 C as shown in The Threshold Sea Surface Temperature Condition for Tropical Cyclogenesis
The role of equatorial waves in tropical cyclongenesis and in this case interaction of equatorial waves with the monsoon trough. Results of filtered OLR as shown in the image below shows the presence of an Equatorial Rossby Wave over those regions and the presence of blue shades indicates negative OLR (enhanced convection).



Source - Tropical Wave Monitoring

This reference The Role of Equatorial Rossby Waves in Tropical Cyclogenesis. Part II: IdealizedSimulations in a Monsoon Trough Environment clearly states that 



  " When just the MT is simulated without the ER wave anomaly fields,
  the MT remains quasi-steady and TC genesis does not occur. It is only
  when the ER wave is imposed on the MT that TC genesis is initiated.
  The results imply that the ER wave–MT interactions produce more TCs
  than would otherwise occur if no such interactions took place."



A question that can be raised  is that  we do know that presence of MJO also promotes tropical cyclongenesis as shown in this reference Diagnosis of the MJO Modulation of Tropical CyclogenesisUsing an Empirical Index. So how can does one state unequivocally that it is a Equatorial Rossby Wave and not the MJO's interaction with the MT that favours tropical cyclogenesis ? 

If we look at the strength of the MJO signal during and after the formation of TC Lam &amp; Maria 

as shown in these set of images 



The amplitude of MJO signal is currently weak (less than 1 being present inside the circle) and is unlikely to be a significant contributor to the formation of tropical cyclones.

This conclusion can be enhanced by looking at the filtered OLR contributions from MJO - 



The presence of positive OLR(in yellow over the Northern/Eastern part of Australia indicating suppressed convection. 
Both the MJO as well as tropical waves favour the formation of twin cyclones as shown by references Dynamical Aspects Of Twin Tropical cyclones  Associated with the Madden Julien Oscillation  and A Case Study of an Outbreak of Twin Tropical Cyclones


Update
In an earlier question that I had asked Relation between direction of shear and cyclone formation one can clearly see a working example of easterly shear favoring the formation of tropical cyclone. So easterly shear as shown in the map below is defined as the difference in the zonal winds at two different pressure levels (850 hPa and 200 hPa). Since by convention easterly winds are noted to be negative increasing positive values of shear is easterly shear(as one travels vertically) and the opposite is westerly shear. The following shear plot is a mean of several days and one can see the easterly shear over the Australian regions where the cyclone formation took place.

$zonal\_shear = U_{850} - U_{200} $

The data is from NCAR NCEP reanalysis.