See also assess software for hints if you want to try something else. Don't get put off by just rectangular grids.

pixel based

Susan Lambiris uses PhotoDeLuxe. It has a simpler interface than PhotoShop and often comes with scanners. The plug-in "Filter Factory" is needed for grids. She claims layers are essential.

Esther Perry says about PhotoShop: "It knows only grids of 45°. To get another angle, adjust width or height (not both) just before printing.
Deborah Robinson sells grids and Torchon elements for CorelDraw and other software. She sells also instructions describing how to use CorelDraw to convert a scanned picture or clipart into a Honiton lace design.
Jo: In the past I used CorelDraw. Good for lace like Rosaline, that only requires lines. For grid laces like Torchon problems arise. The program doesn't know dots (at least in the old version 3.0), small circles could be used in stead. But they have five anchors: centre, top left right and bottom. Usually the wrong one sticks to the grid. This can be overcome with a carefully design library: The basic stitches should carefully snap to one another.
Version 3.0 knows only rectangular grids, I don't know about later versions.

Gimp belongs to the same category as above. It is a G eneral/gnu I mage M anipulation P rogram, available with an open source license. It is primarily developed for Unix-like systems, but (less officially) it also runs on Mac and Windows. Lots of general tutorials on the web, at least one for lace grids in this wiki.

vector based

From an arachne discussion:
A great, free vector drawing program is Inkscape, which has been used for designing diagrams for tatting, but could easily be adapted for bobbin lace. There are a lot of tutorials available online also.
PS by Jo:
At least it is easier to search for tutorials with InkScape and lace than gimp and lace. From their basic tutorial: One of Inkscape's features that set it apart from most other vector editors is its emphasis on keyboard accessibility. This discussion may be more about cutting paper doilies but many principals may be useful, otherwise you might try this suggestion.

Visio also has potentials. Especially once dedicated stencils are developed. Anna Binnie is happy to share hers. Below some baby steps by Jo.