The authors are concerned with (renormalization-) methods for the efficient evaluation of lattice sums of the form \[ S_ n = \sum_{(k_ 1, k_ 2) \in \mathbb{Z}^ 2 \backslash \{(0,0) \}} {1 \over (k_ 1 + ik_ 2)^ n} \quad (n \geq 3) \] and \[ {\mathcal L}^ m_ n = \sum_{p \in \mathbb{Z}^ 3 \backslash \{(0,0,0)\}}Y^ m_ n (\theta_ p, \varphi_ p)/r_ p^{n + 1} \quad (n \geq 3,\;m = 0, \dots, n), \] where \(Y^ m_ n (\theta_ p, \varphi_ p)/r_ p^{n+1}\) is a spherical harmonic of degree \((-n-1)\) and \((r_ p, \theta_ p, \varphi_ p)\) are the spherical coordinates of the lattice point \(p\). The sums \[ \widetilde S_ n = \sum_{(k_ 1, k_ 2) \in \mathbb{Z}^ 2 \backslash {\mathcal N}} {1 \over (k_ 1 + ik_ 2)^ n} \] with \({\mathcal N} = \{(k_ 1, k_ 2) \in \mathbb{Z}^ 2 : | k_ 1 |\), \(| k_ 2 | \leq 1\}\) are calculated approximately by recursion, where the recursion relation is obtained by truncation of \[ \widetilde S_ n - \sum^ \infty_{k=n} (- 1)^{n+k} {\widetilde S_ k \over 3^ k} {k - 1 \choose n - 1} Q_{k- n} = R_ n \] with \[ Q_ n = \sum_{(k_ 1, k_ 2) \in {\mathcal N}} (k_ 1 + ik_ 2)^ n \quad \text{and} \quad R_ n = \sum_{{(k_ 1, k_ 2) \in \mathbb{Z}^ 2 \backslash {\mathcal N} \atop | k_ 1 |, | k_ 2 | \leq 4}} {1 \over (k_ 1 + ik_ 2)^ n}. \] A similar approach is described for the evaluation of \({\mathcal L}^ m_ n\). In both cases, error bounds are given.