A parallel-connected composite with 2–1–2 connectivity and two lead-free single-crystal components was first proposed to highlight its high piezoelectric sensitivity and to describe its large hydrostatic parameters. The first type of the composite layers represents a ferroelectric domain-engineered [001]-poled [Li, (K, Na)](Nb, Ta)O3 single crystal. In the second type of the composite layers, piezoelectric Li2B4O7 single-crystal rods in the form of an elliptic cylinder are regularly aligned in a large polymer matrix. The effective electromechanical properties of the composite were found in three stages, using the effective field and matrix methods that are applicable to piezoelectric media. A new orientation effect was studied that was linked with rotations of single-crystal rod bases in the polymer medium that forms the layers of the second type. Since these rotations are in a Li2B4O7 single crystal with a unique elastic and piezoelectric anisotropy, the layers of the second type exhibit a noticeable influence on the piezoelectric performance and hydrostatic response of the composite. A variation of the aspect ratio of the Li2B4O7 rod base becomes an additional important factor that can improve the hydrostatic parameters of the composite. Some effective parameters of related 2–1–2 composites were compared for a case of different polymer components therein. Three diagrams were first built for the high-performance 2–1–2 [Li, (K, Na)](Nb, Ta)O3 / Li2B4O7 / polyethylene composite to show ranges of rotation angles and volume fractions, which correspond to the longitudinal piezoelectric voltage coefficient g33* > 
500 mV m N-1, hydrostatic piezoelectric coefficient gh* > 200 mV m N-1 and hydrostatic figure of merit dh*gh* > 10-11 Pa-1. These effective parameters are important in piezoelectric sensor, hydroacoustic and other applications of novel lead-free composites.