You are confusing how LAMMPS input works. Fact is that c_COM is a string not a number. To have a command recognize such a string as a reference to a compute instance global vector element and retrieve the value from it has to be programmed into the source code. If this is the case it will be mentioned in the documentation, if it is not mentioned, it is not supported.
Since you can compute the center of mass, you have to have a group of the droplet, which also means that you can restrict its motion by applying a fix spring command to that group with the tether option.
Another option would be to use fix recenter to enforce that the center of mass of the droplet will remain at the same position and all other coordinates translated. This could also be done as a post-processing step using a pre-recorded trajectory using the rerun command.
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