Why "inside" and "lava flow" don't go together
Volcanologists draw a simple line between magma and lava. Magma is molten rock still underground; lava is the same material after it erupts onto the surface. A lava flow is the moving stream of lava on the ground, so by definition it is an outside feature. The 2018 Kīlauea eruption in Hawaiʻi is a clear example: lava flows from the lower East Rift Zone spread over 32.4 square kilometers of land in the Puna District, burying homes, roads, and farmland [1]. That is surface lava, not lava inside the mountain.
What is inside a volcano is the plumbing that feeds such flows. Arenal volcano in Costa Rica has produced more than 500 blocky andesite lava flows since 1968, and geologists describe them as stacked units that build the volcano's outer structure—flows on top of flows, not flows hidden within it [2]. The internal parts are the conduits and chambers that supply the eruptions.
Where lava flows actually appear on a volcano
Most lava flows start at fissures or vents on a volcano's flanks or inside its summit caldera. At Piton de la Fournaise on Réunion Island, about 95% of roughly 250 historical eruptions since 1708 occurred inside a large horseshoe-shaped caldera called the Enclos, and eruptions are typically fissure-fed, forming extensive flow fields [5]. The hazard map for that volcano shows the highest future flow probabilities inside the Enclos, with some areas up to 12% [5]. That is still surface ground inside a depression, not lava circulating within the mountain.
Some flows travel far beyond the volcano. Etna's A.D. 1669 flank eruption sent a huge lava flow into the city of Catania, and prehistoric flows also reached what is now the urban district [3]. The point is the same: the lava was on the outside, moving across the landscape.
What the old flows tell us about a volcano's history
Ancient lava flows are studied as layers on the volcano's surface and surroundings. Paleomagnetic dating—reading the direction of Earth's magnetic field recorded in cooled lava—lets scientists place these surface flows in time. In Catania, three Holocene flows were dated this way; two of them, at San Giovanni Galermo and Larmisi, appear to be parts of a single lava field erupted between about 5,494 and 5,387 years ago [3].
The same approach works on Kamchatka's Avacha volcano. Three lava flows there were dated: two on the Young Cone formed in 1827 and roughly 300–600 years ago, while a flow on the somma crest is about 30,000–32,000 years old [4]. These are all flows that reached the surface and cooled there, later becoming part of the geological record.
Sources used in this answer
Damage assessment for the 2018 lower East Rift Zone lava flows of Kīlauea volcano, Hawaiʻi
The 2018 lower East Rift Zone eruption of Kīlauea produced lava flows that inundated 32.4 km² of land and destroyed or damaged thousands of structures in the Puna District.
The blocky andesitic lava flows of Arenal volcano, Costa Rica
Arenal volcano in Costa Rica has produced more than 500 blocky andesite lava flows since 1968, which stack into larger geological units that build the volcano.
Paleomagnetic dating of prehistoric lava flows from the urban district of Catania (Etna volcano, Italy)
Paleomagnetic dating of prehistoric lava flows exposed in Catania's urban district shows some are about 11,000 years old and others form a single lava field erupted roughly 5,400 years ago.
Dating of lava flows of the Avacha volcano, Kamchatka, from paleomagnetic data
Paleomagnetic data date three lava flows on Avacha volcano to 1827, 300–600 years ago, and about 30,000–32,000 years ago.
Lava flow hazard map of Piton de la Fournaise volcano
At Piton de la Fournaise, about 95% of historical eruptions occurred inside the Enclos caldera, and the lava flow hazard map shows the highest future flow probabilities there.