Some simple 3D forms can be made by extruding or revolving 2D curves in Illustrator. Then one can map patterns on the generated surfaces, but there's very little control on how Illustrator wants to place them. Inkscape has not even this.
You can create 3D-looking patterns by blending in Illustrator. Inkscape has "Interpolate" which is quite the same. Then there's the envelope distortion in Illustrator and a drastically limited version of it in Inkscape. With them you can bend clouds of lines or curves. The result may resemble something 3D surface if you are lucky and in addition you have a goal which happens to be possible to be made in that way.
But if you have an already decided "I want it" 3D form which is not an extrusion or revolved surface you generally have no other possibility to present it as a cloud of curves other than drawing every curve manually. Artists have done it hundreds of years, but developing the needed skills takes years (assuming the person has got in birth what the job takes).
3D programs are useful if the program allows and the user knows how to generate the wanted 3D surface. Your half-sphere is simple. Only to generate such line pattern which shows the 3D form also in the straight top view needs some thinking. One possibility is to split a solid with non-parallel planes and then to use the splitting borders as the image.

The image is just before the splitting. The solid is a half sphere on a plate.
After using the split body function and hiding the splitting planes the top view in wire frame rendering mode looks right - except there's no straight lines in the left and right and there's a circle which should be removed.

I took the curves into Illustrator, deleted the unwanted parts with the shape builder, inserted a couple of straight vertical lines and changed the stroke width:

The curved parts are pieces of ellipses. One who knows some elementary geometry could calculate the right ellipses and draw them in 2D from the numeric measures. A talented and well trained draughtsman may see the right ones without any math. But a 3D program gives them with very low effort, as shown above.
If you want to go to 3D software to make something substantially more complex than what's got by applying a 3D geometry creation primitive like extrude, revolve, sweep, loft, cut etc... you take a new challenge: It's far from trivial to learn to model something complex, say cartoon figures, realistic curved surface vehicles, animals, etc... Creating them from scratch needs same abilities as sculpting.