Cubic La(FexAl1-x)13 intermetallic compounds can be stabilized with iron concentration x between 0.46 and 0.92 in the NaZn13-type structure (D23) with Fm3c (Oh6) space-group symmetry. Here the Fe-Fe coordination number can increase up to 12. At low x values, a mictomagnetic regime occurs with distinct cusps in the ac susceptibility. With the increase of the iron concentration, a soft ferromagnetic phase is found which at lower temperatures shows anisotropy effects related to reentrant mictomagnetic behavior. Finally, for x>0.86, antiferromagnetic order appears along with a sharp metamagnetic transition in external fields of a few teslas. The saturation magnetic moment increases linearly with x from 1.4B/Fe to 2.1B/Fe throughout the ferromagnetic and antiferromagnetic regime. The breakdown of long-range ferromagnetic order at high x values can be explained by modifications of the iron moment and their coupling at a large Fe-Fe coordination number. However, with application of a magnetic field, the ferromagnetic state can be fully recovered. The room-temperature resistivity decreases with increasing x from 200 to 160 cm. The low-temperature slope d/dT is related to the magnetic order, being negative in the antiferromagnetic state and positive in the ferromagnetic state. The metamagnetic transition causes a decrease of the resistivity of about 20% and a sign change in d/dT. This behavior is discussed in terms of the two-current model. The thermal expansion exhibits a strong Invar character and is described by a combined band and local-moment model which allows calculations of corresponding magnetovolume coupling constants. The metamagnetic transition causes a large magnetic striction.