The paper is concerned with some abstract sequential lower semicontinuity results for integral functionals defined on functions taking values in infinite-dimensional spaces. The results obtained are also applied to get sequential lower semicontinuity results for functionals defined on the set \({\mathcal A} ([0,1 ],V)\) of the absolutely continuous functions from \([0,1 ]\) to the reflexive Banach space \(V\). If \(\Omega\) is a \(\sigma\)-finite complete measure space, \(V\), \(W\) are reflexive Banach spaces, \(X\subseteq L^\infty (\Omega, V)\), \(Y\subseteq L^1 (\Omega, W)\), \(L: (t,x, y)\in \Omega\times V\times W\to L(t, x, y)\in \mathbb{R}\cup \{+\infty \}\) is measurable with respect to the product of the \(\sigma\)-algebra of \(\Omega\) and of the Borel \(\sigma\)-algebra in \(V\times W\) with \(L(t, \cdot, \cdot)\) sequentially weakly lower semicontinuous for a.e. \(x\in \Omega\) and \(L(t, x, \cdot)\) convex for a.e. \(x\in \Omega\) and every \(x\in X\), define the \[ I: (x, y)\in X\times Y\to \int_\Omega L(t, x(t), y(t)) dt, \] \[ H(t, x, p)\in \Omega \times V\times W'\to \sup\{\langle p,w \rangle- L(t, x,w): w\in W\} \] and consider the following assumptions: (1) \(\exists\varphi: \Omega\times [0,+ \infty]\times [0,+ \infty]\to \mathbb{R}\) with \(\varphi (\cdot, r,s)\in L^1 (\Omega)\) \(\forall r,s\) such that \(\sup \{H(t, x, p): |x|\geq r\), \(|p|\geq s\}\leq \varphi (t, r, s)\), (2) \(\forall\{x_n \}\subseteq X\), \(\{y_n \}\subseteq Y\) with \(\sup\{I (x_n,y_n): n\in \mathbb{N}\}< +\infty\) \(\{(L(\cdot, x_n (\cdot), y_n (\cdot )))^-\}\) is weakly precompact in \(L^1 (\Omega)\). The following results are proved: if (1) holds then \(I\) is sequentially lower semicontinuous in \(X\times Y\), if \(L\geq 0\) then \(I\) is sequentially lower semicontinuous in \(X\times Y\), if (2) holds then \(I\) is never \(-\infty\) and sequentially lower semicontinuous in \(X\times Y\). Finally, it is proved that if \(\forall \{x_n\} \subseteq {\mathcal A} ([0,1 ], V)\) with \(x_n\to x\) weakly and \[ \sup \biggl\{\int_\Omega L(t, x_n (t), x_n' (t))dt,\;n\in \mathbb{N}\biggr\}< +\infty \] \(\{(L(\cdot, x_n (\cdot), x_n' (\cdot)))^-\}\) is weakly precompact in \(L^1 (\Omega)\), then \[ x\in {\mathcal A} ([0,1 ], V)\to \int_\Omega L(t, x(t), x' (t))dt \] is weakly sequential lower semicontinuous. Some examples are also discussed.