Unfortunately, a lattice description with and without knowledge of structure and symmetry is not uniform.
No crystal structure data available (e.g. CALM)
If one determines only the lattice parameters, e.g. by means of XRD, then the recommendation for triclinic applies:
\begin{align*}
a \leq b \leq c \quad \textrm{and} \quad \alpha, \beta, \gamma >90\degree
\end{align*}For monoclinic the physical axes setup is valid:
\begin{align*}
a\leq b \quad \textrm{and} \quad \gamma>90\degree
\end{align*}although more common is still the mineralogic axes setup with β different from 90°.
The internationally accepted recommendation for orthorhombic is:
\begin{align*}
a\leq b\leq c
\end{align*}For all higher-symmetric crystal systems no rules are required since there are no reasonable axes permutations.
The reason for these rules is that a phase search in tables (Hanawalt or Fink index) or databases can be significantly shortened [1].
In addition, (phase-specific) information such as the lattice parameter ratios a / b : 1 : c / b are then unambiguous.
Data from crystal structure databases
However, if the crystal structure of a phase is known, the upper rules are obsolete.
Then the definition of axes and angle definition follows the alignment of the symmetry elements, as specified in the standard settings of the space-group types in the International Tables for Crystallography (Vol. A).
Since also in CALM only the crystal lattice is determined, this means that the rules listed above are followed.
Thus, even for correctly described lattices of low-symmetry phases, there will inevitably be differences from their descriptions listed in databases.
Thus, for orthorhombic phases, a, b and c can be interchanged arbitrarily, while the output in CALM will always show:
a < b < c.
[1] Faber, J.; Weth, C. & Jenkins, R.:PCSIWIN: A Windows-Based Index Program with Hanawalt, Fink and Alphabetic Search Capabilities for Use with the ICDD Powder Diffraction File (PDF), Mater. Sci. Forum, 378-381 (2001), 106-111