High-thermal-conductivity (λ) nanocomposites have been thought to resolve thermal management issues in electronic development. However, use of these is still challenging due to the easy aggregation of micro/nanofillers in a matrix. Here, a high-efficiency, low-cost, environmental strategy was developed wherein pyrene-functionalized alkali lignin (AL-PPBA) dispersants were employed to disperse hydroxylated boron nitride nanosheets (BNNS) by π–π conjugation in a cellulose nanofiber (CNF) solution, following which a nanocomposite film was prepared via the vacuum-assisted self-assembly method. Experimental and simulation results show that an efficient interfacial interaction between AL-PPBA and BNNS was achieved successfully and a stable aqueous dispersion solution was obtained. The as-prepared nanocomposites thus show λ as high as 18.27 W m–1 K–1 with the loading of 10.4 vol % of BNNS and superior anisotropy. A potential thermal management capability was demonstrated when using nanocomposites as heat sink components for light-emitting diode (LED) chips. This study provides a route to promote the dispersity of micro/nanofillers via a noncovalent cross-linking strategy and address heat management issues.