"further lack" is a grammatically correct and usable phrase in written English.
You can use it when discussing something that is already deficient in some way and requires additional deficiency in order to be complete. For example, "The financial situation of the company was already desperate, and further lack of funds only made the situation worse."
Japanese bosses argued that we would be diminished if we didn't join the euro so similar warnings about the referendum further lack credibility".
In particular, the agency cited the "fluid political dynamics" of Rousseff's leadership and a "further lack of cohesion within the president's cabinet.
To complicate his life further, lack of air conditioning plays havoc with summer staffing: the union contract specifies that when the temperature exceeds 90 degrees Fahrenheit, as it did Wednesday, workers are to have four-hour rather than seven-hour shifts.
Further, lack of interrater reliability may compromise the use of CMS in interpreting health state ratings.
Further, lack of adequate canteen facilities influenced the selection of food on offer, food safety and capacity.
Further, lack of clinical detail in both disease etiology and severity may lump heterogeneous patient groups into the same disease category.
Further, lacking decorum and discipline, Trump exhibits only a dim understanding of domestic and foreign relations.
The study further lacks in being a one-time cross-sectional analysis and hence all our results are open to evidence testing.
Our results show that extant great apes exhibit rod-like PDPs with barely discernible muscular impressions on the palmar side, further lacking developed tufts and associated palmar pads (Figures 2 4; see also [4], [6], [22]).
For example, F. succinogenes is missing the genes necessary for xylose and xylodextrin transport (i.e. a xylose permease) into the cell, and further lacks a xylose isomerase (EC 5.3.1.5) to convert xylose into xylulose.
Further, lacking cytosolic bacteria, the systemic circulating LPS is unlikely to be present inside the cells at high enough dosage to release the histones from the droplets.
