Apparently when spawning a new LanguageClient, the serverOptions field includes a field called options of type ForkOptions. This allows the setting of stack size in forked processes.

The final configuration:

const node = require('vscode-languageclient/node'); 
... 
const serverOptions = {     
    module: serverModule,      
    transport: node.TransportKind.ipc,     
    options: {  
        execArgv: ['--stack-size=8192'],    
    } 
};