So I haven't found any answer to it, except it can't be done via CSOM.
But I have found workaround, and it goes like this:
Why I want to use CSOM anyway? My goal was to transfer list content into new SharePoint site, and any other way to copy list, for example using Export/Import-SPWeb didn't include very important lookup field. Lookup field can be imported using CSOM, so my decision was based on that. But CSOM don't support versioning. So the workaround was to do the Export/Import using PowerShell first. This would include multiline field with versions, but missed lookup field. But then, afterwards I'm able to update only lookup field using CSOM, and still preserving versions imported as a first step.
This is not the direct answer to question above, but might provide some solutions to people struggling with same problem.
PowerShell export command:
Export-SPWeb -Identity http://source-host -Path C:\export_list.cmp -ItemUrl /Lists/ListTitleForExport -IncludeVersions All
PowerShell import command:
Import-SPWeb -Identity http://target-host -Path C:\export_list.cmp -Force -Verbose -IncludeUserSecurity -ErrorAction Continue
Last advice - if, after importing using PowerShell, your lookup column is broken you will have to delete and create this column again.