globe with grid lines

You can add a image and then trace it. In Illustrator with image trace you can make raster to vector.

To elaborate:

Draw the outer circle first. Use a stroke color but no fill. You can change the fill later.

Copy > Paste in Front.  You will have 2 circles, both the same size and in the same position.

Copy > Paste one of the circles and set the 3rd circle out of the way for the time being.

Select the top circle (from the set of 2 circles on top of each other). Hold down Alt/Option and drag a side handle towards the center.

Select the large circle and the ellipse in the center.

Choose Object > Blend > Blend Options and type 2.

Choose Object > Blend > Make.

Now you can do the same type of procedure for the next lines.

Draw a straight horizontal line through the center.

Draw an ellipse at the top.

Select the ellipse and choose Object > Path > Offset Path.

Select both of the top ellipses. Select the Reflect tool.

Alt/Option click the center of the circle to set the origin point for the reflection.

Select Horizontal and click Copy.

You end up with this:

Select one of the ellipses and use the Scissors tool to click where the ellipses intersect the globe. Repeat for all 4 ellipses.

Use the Direct Selection tool to select and delete the extra parts.

If you search on the web, you might also be able to find a script that does this automatically.

The longitudes:

draw two ellipses (a wide one and a very narrow one), center them and then use a blend.

How to blend objects in Illustrator

The latitudes:

a straight line for the equator, two ellipses and then mirror them