The problem here is that, as is often the case on FT, the facts are obscured by irrelevant anecdotes. The facts are critical. This fact pattern involves a Syrian passport transiting Germany enroute the US.
Others have provided examples of US passports and kindnesses done them by various and sundry LH employees, border personnel and the like. Those are either irrelevant or simply examples of individuals breaking their employers' rules.
The fact remains that Syria, and only Syria determines whether and how its passports are signed. Germany and only Germany determines whether individuals presenting themselves for entry (or transit) must possess a signed passport.
Apparently Syria laminates over the signature block, presumably meaning that one must sign the passport at some official location and then have the laminate applied. This is not so for, by way of example, US passports. These arrive in the mail with a blank signature block, the advice to sign and may be signed at any point. That is the respective prerogative of Syria and the US.
GA's, local security contractors and other customer-facing personnel are neither lawyers, judges nor border guards. Their sole function, and it is drummed into their heads routinely, is to protect their employer, LH in this case, from delivering passengers who lack proper documents as that may cause LH to be fined.
Thus, whether OP's friend has been admitted to Germany multiple times on that unsigned passport, been granted multiple visas by Germany is irrelevant. The fact is that the friend lacked a signed and signable passport.
As such, the passenger presented himself without proper documents and was properly denied boarding.
Rather than pursuing EC 261/2004 compensation, the friend (not OP, but the friend), ought to throw himself at LH's mercy, admitting 100% fault, and ask that LH consider allowing him to use the value of the ticket against the cost of a new ticket or somesuch. It is unlikely that LH will be forthcoming, but it is more likely to be fruitful than an EC 261/2004 claim in this circumstance.