Multisomes are multicompartmental structures formed by a lipid-stabilized network of aqueous droplets, which are contained by an outer oil phase. These biomimetic structures are emerging as a versatile platform for soft matter and synthetic biology applications. While several methods for producing multisomes have been described, including microfluidic techniques, approaches for generating biocompatible, monodisperse multisomes in a reproducible manner remain challenging to implement due to low throughput and complex device fabrication. Here, we report on a robust method for the dynamically controlled generation of multisomes with controllable sizes and high monodispersity from lipid-based double emulsions. The described microfluidic approach entails the use of three different phases forming a water/oil/water (W/O/W) double emulsion stabilized by lipid layers. We employ a gradient of glycerol concentration between the inner core and outer phase to drive the directed osmosis, allowing the swelling of lamellar lipid layers resulting in the formation of small aqueous daughter droplets at the interface of the inner aqueous core. By adding increasing concentrations of glycerol to the outer aqueous phase and subsequently varying the osmotic gradient, we show that key structural parameters, including the size of the internal droplets, can be specifically controlled. Finally, we show that this approach can be used to generate multisomes encapsulating small-molecule cargo, with potential applications in synthetic biology, drug delivery, and as carriers for active materials in the food and cosmetics industries.