For laser cutting you only want single cutting lines. Otherwise, the lines will literally be cut multiple times, which is not the best for your material or for the machine. 

Often double lines occur where people have placed parts hard up against one another and not deleted the overlapping lines. Shared cutting lines between parts will only reduce costs if you delete duplicates.

If finding and deleting duplicates looks like a bit too much work - simply moving objects apart may be an easier/faster way to resolve doubled up lines between parts. 

First up is AutoCAD - Scroll down to see how to remove duplicate lines in Fusion, Illustrator and Inkscape.

AutoCAD has a great feature for removing doubled up or overlapping lines. Choose Delete Duplicate Objects from the Modify menu or type Overkill the command line.

Please note that if you have overlapping lines in an array or object the overkill command might not pick them up. You may need to EXPLODE everything (might need multiple passes) until it is bare lines then use OVERKILL.

Modify Menu Users:

Select all the objects in your drawing or just the objects you wish to combine. Then from the Modify menu select Delete Duplicate Objects.
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The following dialog box opens.

Ensure the Optimize polyline segments option is checked. If you have "do not break polylines" checked the feature will not break native shapes such as square etc. Uncheck this option to ensure all the duplicates are removed.

The Object Difference Tolerance box determines how exact two objects must be to be considered duplicates. The default, 0.000001, deletes almost exact objects. You can change this to 0, to delete only objects that are exactly on top of each other.

The "Optimize polyline segments" check box, on by default, removes duplicate line or arc segments within a polyline, or lines and arcs that overlap a polyline. If you uncheck this, the command only removes duplicates of entire polylines.

The "Combine co-linear objects that overlap" check box, also on by default, combines objects that partially overlap into one object.

The "Combine co-linear that are end-to-end" check box combines objects that don’t overlap, but are end to end, such as two co-linear lines with one common endpoint.

Command line users:

The OVERKILL command, part of Express Tools, can help. This command deletes duplicate objects and goes further to combine overlapping lines and arcs.

When you start the command, the next prompt is Select objects: and you can type all and press Enter to apply the command to the entire drawing. Then press Enter again to end object selection.

To keep the default settings, just click OK. 

You can specify lots of settings to control the process. For example, you can check the Ignore LAYERS check box to delete overlapping lines, even if they are on different layers.

The Object Difference Tolerance box determines how exact two objects must be to be considered duplicates. The default, 0.000001, deletes almost exact objects. You can change this to 0, to delete only objects that are exactly on top of each other.

The "Optimize polyline segments" check box, on by default, removes duplicate line or arc segments within a polyline, or lines and arcs that overlap a polyline. If you uncheck this, the command only removes duplicates of entire polylines.

The "Combine co-linear objects that overlap" check box, also on by default, combines objects that partially overlap into one object.

The "Combine co-linear that are end-to-end" check box combines objects that don’t overlap, but are end to end, such as two co-linear lines with one common endpoint.

Click OK to execute the command.

Unfortunately there is no magic tool for deleting them automatically, but this forum post shows a way to identify them in your drawings so you can select and delete them manually:

https://forums.autodesk.com/t5/fusion-360-design-validate/cleanup-duplicate-sketch-elements/td-p/5720772

In Illustrator, you will likely see duplicates as being a darker to the other lines on screen (thin 0.01mm strokes tend to show this best).

Use the Direct Selection tool to click on each of these lines, and hit delete twice. It should leave another line behind, paler than the one you had and the second delete action will remove any stray anchor points.

If you have three or more sets of duplicate lines you will need to repeat this process several times to get all the extra lines. 

* Pro tip - If you've traced an image to convert it to vectors in Illustrator, make sure to tick the ignore white box to prevent double lines being generated. Double lines can be time consuming to remove so avoiding them in the first place is always best.

In Inkscape, you will likely see duplicates as being a darker to the other lines on screen (thin strokes tend to show this best).

If you have three or more sets of duplicate lines you will need to repeat this process several times to get all the extra lines.

Before you begin: Select All and use the Path > Object to Path command.

Step 1: Select the Edit Paths by Nodes tool.

Step 2: Click on an object that contains a double line and then select a node on one side of the double line to be removed.
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Step 3: With the node highlighted dark gray, click the Break Path at Selected Nodes button

Step 4: Click on the node on the other side of the double line, and use the Break Path button again.
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Step 5: Click on the line between the two nodes so that both nodes are highlighted dark gray and a larger size to the rest of the nodes in the object, and press delete. A paler blue line should be left behind.
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Step 6: Select the nodes on each side of the next line, and repeat the above process.

Hope that helps you produce great designs for laser cutting! Please do let us know if you have tips or questions about reducing duplicate lines in your chosen design software.