When it comes to laser phenomena in quantum-dot-based systems, usually atomic models are employed to analyze the characteristic behavior. We introduce a semiconductor theory, originating from a microscopic Hamiltonian, to describe lasing from quantum dots embedded in microcavities. The theory goes beyond two-level atomic models and includes modified contributions of spontaneous and stimulated emission as well as many-body effects. An extended version, which incorporates carrier-photon correlations, provides direct access to the photon autocorrelation function and thereby on the statistical properties of the laser emission. In comparison to atomic models, we find deviations in the dependence of the input/output curve on the spontaneous emission coupling . Modifications of the photon statistics are discussed for high-quality microcavities with a small number of emitters.