Two-lobe Lanczos is fine. It’s Lanczos (or any other sinc-based filter) with more than two lobes that gets problematic.
However, if you’re going to use 2-lobe Lanczos, you might as well use Catmull-Rom [bicubic] since as mentioned previously the two are virtually identical. The reason you see any difference between the Lanczos filter and the “bicubic” filter in various image processing apps is that the bicubic they are using is generally not Catmull-Rom. Typically it’s a Mitchell-Netravali filter with the coefficients tweaked to be “sharper.”
Can you tell that I like Catmull-Rom a lot? I do. I like Lanczos2 as well, but again, the two are practically identical.