How can I create this curvilinear element?

I’d make a couple of appropriate bezier curves then use Tig’s Extude tools to create the formwork on which you can use follow me, or a pipe extension or even replace the edges with tube components.
TigLattice

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I’d also suggest “profile builder” to make the tubing (the free, and less functional version, on smustard will do this). The benefit of this is that you can apply any tubing profile/size to all the lattice lines all at once and subsequently change the diameters globally if needed, to different sizes or even shapes if desired. The surrounding frame would be a separate group.
Also would be worth noting that the amount of rails is going to depend on the line/curve’s segments, which would need to be figured out prior to extrusion.

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