It is possible. You also need someone that is above or horizontal of the person you are building the Lazarus of. So a cousin that is not a direct descendant of the individual. Here are some links describing Lazarus and highlighting some uses.
Here is the Lazarus Description on GEDmatch Wiki:
Lazarus
Create surrogate DNA kits of close ancestors.
Designed to re-create a target kit# DNA profile by combining the matching segments between a deceased person's descendants and their other relatives (ancestors, siblings, aunts, uncles, etc.).
While not specifically designed to work with half-siblings, they can be used as descendants too since the same concept applies. It will produce a kit containing the DNA data common to both half-siblings, corresponding to their common parent.
Lazarus kits typically contain much less DNA data than normal kits (though, not always), but may be useful nonetheless.
The more close relatives' kit#s you have - the better your results will be. You can also use more distant cousin matches, but it will likely take many more. In extreme cases, it's not unheard of to use over 100 kit#s to produce a single Lazarus kit.
What can I do with a Lazarus produced kit?
You can use a Lazarus produced kit# in the comparison tools like any other kit#. You can reconstruct a recent ancestor and use matches to their Lazarus kit# to identify distant cousins related through them. For the one to many tools there is a minimum data threshold - your Lazarus kit# must have over 1500cM of DNA data to be eligible for batch-processing needed for the one to many tools.
Data Entry and Choice of Thresholds
You must have at least one kit in Group 1 (Descendants) and one kit in Group 2 (Other Relatives).
It is not necessary to add data for every blank on the entry form, but more data usually produces better results.
If you have a Kit# for the Target Kit#'s partner this can also be used to increase accuracy (must be the other parent of all descendants used in Group 1)
Group 1 is close descendants (son, daughter, or perhaps grandchild) and Group 2 is siblings, cousins, aunts/uncles, or parents of the target person for whom you want to recreate the DNA. Each kit can provide a piece of the DNA for the resulting target kit.
One example using 2 siblings in Group1, and 3 aunts/uncles in Group 2, was able to achieve almost 100% restoration of a full SNP count of a parent.
If close relatives are not available distant matches can be used in Group 2 but less Lazarus DNA data will be produced - you may still be able to create a virtual cousin - instead of the hoped for virtual parent.
There is no additional benefit from putting both children and grandchildren in Group 1. Use the person closest to the Target Kit# (the child of the target) if they are available.
The default included segment size thresholds, 6cM, 700SNPs, are a good starting point. You can triangulate small segments in the One-to-one tool between the relatives to check the validity of smaller segments to see if smaller thresholds could be used to yield more Lazarus DNA. As always, using smaller segments increases the chance of including random deep ancestry segments and IBS (Identical by State), false positives.
Example: Using Lazarus to reconstruct Paternal Kit# from Distant Cousins, Maternal Spouse Kit# and 2 Daughter Kit#s
Use the People who match one or both of two KIT#s tool. Use one daughter Kit# (for the descendant), and the mother (as the target Kit#'s partner). The application gives 3 lists. Use the results that match the daughter, but not the mother. The resulting list will be the ones that are related to the target father. Also, keep a copy of the list of the top few matches to the mother and daughter. Click the check marks for the top 98 matches (or fewer if you get tired of clicking) to daughter only (and not mother). Click the "Submit" button at the top of that section. It will bring up a menu with several "Visualization options". The last option is Lazarus. Select Lazarus. It will have all of Group 2 filled in, with daughter and mother as the first 2. Move daughter kit number from group2 to group 1. Add the other sister to group 1. Move your mother to spouse. Generate your Lazarus kit.
Do some trial one-to-one comparisons to make sure the resulting Lazarus kit does not match the ones (from above) that match your mother and you. If you find any kits that should not match, look at the results page from Lazarus, and find the kit(s) that contribute to the matching segments. Remove the offending kit(s), and run Lazarus again. Repeat until it gives the expected results. Delete any of the kits that didn't work out.
Evaluate and Revise your results:
After you generate a Lazarus kit, you should test the results to ensure that they are consistent with your expectations.
1. Use the one-to-one utility to compare the resulting kit with your own kit, to ensure that it is a perfect match.
2. Compare the results with a kit on the other side of the family, that should not match. If you find any matching segments, look at the "Contributions" list on the results page to see what kit(s) the matching segment(s) came from. Remove that kit from your entry form, and generate new results.
Notes:
It is generally a good idea to print (or otherwise save) the input form before starting processing. Usually, this is an iterative process where you need to go back and change 1 or 2 entries and run the program again. Select the 'Trial Run' option for the first few attempts, until you feel like the results are good enough to generate a test kit and start evaluating it.
When the new surrogate parent kit has been created, it should be verified by comparing it with yourself, and with cousins known to be on the branch of your other parent. A parent should be a perfect match with their child. It should not match any segments with the other parent or cousins related to the other parent, unless you have reason to believe there has been a recent intermarriage.
Created kits must contain at least 1500 cM total segment length before they will be eligible for batch processing. Smaller kits may be used only for one-to-one matches.
If you create a replacement or revised kit, please delete the old one to reduce the clutter (and the load on the servers). Thanks.
Lazarus Kit#s not showing on One-to-many results.
There are 2 kinds of Lazarus kits. The ones with Kit numbers starting "LL" have at least 1500 cM of segments, and the ones with kit numbers starting "LX" have less than 1500 cM. The LX kits do not have enough information to provide valid one-to-many matches, so they do not show up in the one-to-many report. Another thing that would have caused that would be if "no batch processing" was selected for "Processing" on the entry form when you entered your data.
Caveats:
The resulting surrogate kit does not contain any SNPs for segments where there was no reference data. You must keep this in mind when evaluating any results from the use of this kit.
A blog describing Lazarus: https://dna-explained.com/2015/01/14/lazarus-putting-humpty-dumpty-back-together-again/
There is also a closed Facebook group for GEDmatch Lazarus. Here is the link: https://www.facebook.com/groups/818555341528048/
