Chemically synthesized near-infrared to mid-infrared (IR) colloidal quantum dots (QDs) offer a promising platform for the realization of devices including emitters, detectors, security, and sensor systems. However, at longer wavelengths, the quantum yield of such QDs decreases as the radiative emission rate drops following Fermi's golden rule, while non-radiative recombination channels compete with light emission. Control over the radiative and non-radiative channels of the IR-emitting QDs is crucially important to improve the performance of IR-range devices. Here, we demonstrate strong enhancement of the spontaneous emission rate of near-to mid-IR HgTe QDs coupled to periodically arranged plasmonic nanoantennas, in the form of nanobumps, produced on the surface of glass-supported Au films via ablation-free direct femtosecond laser printing. The enhancement is achieved by simultaneous radiative coupling of the emission that spectrally matches the first-order lattice resonance of the arrays, as well as more efficient photoluminescence excitation provided by coupling of the pump radiation to the local surface plasmon resonances of the isolated nanoantennas. Moreover, coupling of the HgTe QDs to the lattice plasmons reduces the influence of non-radiative decay losses mediated by the formation of polarons formed between QD surface-trapped carriers and the IR absorption bands of dodecanethiol used as a ligand on the QDs, allowing us to improve the shape of the emission spectrum through a reduction in the spectral dip related to this ligand coupling. Considering the ease of the chemical synthesis and processing of the HgTe QDs combined with the scalability of the direct laser fabrication of nanoantennas with tailored plasmonic responses, our results provide an important step towards the design of IR-range devices for various applications.