Analysis of subionospheric VLF transmissions, observed in relation with sprites, has led to the identification of a new category of VLF perturbations caused by the direct effects of tropospheric lightning on the overlying lower ionosphere. They constitute a large subset of the so-called "early/fast" events where now the term "fast," which implies rapid onset durations less than ~20 ms, does not apply. In contrast with early/fast, the perturbations have a gradual growth and thus "slow" onset durations ranging from about 0.5 to 2.5 s; thus these events are labeled herein as "early/slow." They are indicative of a new physical process at work which, following a sprite-causative cloud-to-ground discharge, leads to a gradual buildup of conductivity changes in the lower ionosphere which must be responsible for the long onset durations of the observed perturbations. Analysis of broadband VLF sferic recordings, made with a two-channel receiver near the sprite producing storms, shows that the growth phase of an early/slow event coincides with the occurrence of complex and dynamic lightning action. This is composed of a few sequential cloud-to-ground lightning strokes and clusters (bursts) of sferics which are attributable to intracloud lightning. We postulate that the long onset durations are due to secondary ionization buildup in the upper D region below the nighttime VLF reflection heights, caused mainly by the impact on sprite-produced electrons of sequential electromagnetic pulses radiated upward from horizontal in-cloud discharges.