In general, no. It may be possible in some special cases where the lava contains embedded organic material plants and animals that were caught in the lava flow , or where there are significant inclusions of air due to carbon dioxide in the air. But the rock that makes up lava has very little carbon content, and it wouldn't necessarily be of any help in dating it anyway, since it came from underground and was only very briefly exposed to atmospheric 14C. Lava itself does not contain much carbon and comes from material too old for there to be detectable levels of carbon It is possible, though, to use carbon dating if there are remnants of organic matter that was trapped under a lava flow.
When miners were sinking a ventilation shaft for the new Crinum Coal Mine in Central Queensland in see map below they unearthed a rare find. After digging through the thin surface sands and clays, followed by basalt, 21 metres almost 69 feet down they found pieces of wood entombed in the bottom basalt flow. The wood was in three states—ash, charred, and intact. So how could these tree trunks have survived being engulfed by molten lava?
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Here I want to concentrate on another source of error, namely, processes that take place within magma chambers. To me it has been a real eye opener to see all the processes that are taking place and their potential influence on radiometric dating. Radiometric dating is largely done on rock that has formed from solidified lava. Lava properly called magma before it erupts fills large underground chambers called magma chambers. Most people are not aware of the many processes that take place in lava before it erupts and as it solidifies, processes that can have a tremendous influence on daughter to parent ratios.