Is there any reason to think the result would be radically different than for blood? (E.g., hemoglobin). As the first comment points out, the lungs need about 70 m^2 of surface area.
So as long as the surface area of the trapped bubble-seawater interface was at least that size, perhaps you could survive indefinitely, down to the limit of air-breathing depths.
In smaller bubbles, perhaps you could keep yourself alive by splashing. Like an aquarium bubbler in reverse.
The problem is that the diffusion coefficient in the lungs is different than that for an air-water interface. Consider (as an extreme example) a bubble surrounded by steel with a surface area of 70 m^2. Yes, there is still diffusion of oxygen through the steel, but it's at a vastly lower rate than it is through water.
http://publishing.cdlib.org/ucpressebooks/view?docId=kt167nb...In studies of the distribution of dissolved gases in the sea it is generally assumed that, whatever the location of a water particle, at some time it has been at the surface and in equilibrium with the air. In their studies of the dissolved nitrogen content Rakestraw and Emmel (1938a) have found that the water is virtually saturated (referred to a normal atmosphere), regardless of depth; therefore this assumption appears valid and also indicates that biological activity involving either fixation or production of nitrogen cannot be sufficient to affect significantly the concentration of this gas in the water. As the waters of the oceans appear to have been saturated with oxygen and carbon dioxide at some stage in their history when they were at the surface, the differences between the saturation values (computed from the temperatures and salinities) and the observed contents are measures of the changes which have been effected by biological agencies. The factors influencing the distribution of carbon dioxide are discussed in the following sections, and the distribution of dissolved oxygen will be considered in many places in the ensuing chapters.
So as long as the surface area of the trapped bubble-seawater interface was at least that size, perhaps you could survive indefinitely, down to the limit of air-breathing depths.
In smaller bubbles, perhaps you could keep yourself alive by splashing. Like an aquarium bubbler in reverse.