There is no such thing as upgrading to prem eco on LH, you will directly WL for business.
You need a LH flight number, not a UA flight number. You will need the account login info, there is no way around that. Once logged into the 1K account then the ‘upgrade with +P’ form that you already found will work. Simply add name, route and flight number. UA cannot do this for you, your boss or someone with knowledge of the account info needs to do it. That’s all that is needed. Might go on the WL, but LH clearance rates are very high.