Solid-state lighting devices including light-emitting diodes (LEDs) and lens arrangements for packaged LED devices are disclosed. An LED package may include one or more LED chips on a submount with a lens positioned on the submount to form a cavity. The one or more LED chips may reside in the cavity without direct encapsulation materials that would otherwise contact the one or more LED chips and any corresponding wirebonds. In this manner, the one or more LED chips may be driven with higher drive currents while reducing degradation and mechanical strain effects related to differences in coefficients of thermal expansion with typical encapsulant materials. LED packages may also be configured with one or more apertures that allow air flow between an interior volume of a cavity and an ambient environment outside the LED package to promote heat dissipation at higher drive currents.