No, but you still might be allowed to do what you ask in the subtext.
You cannot change the license of (L)GPL - covered code, if you didn't write it.
What you can do, of course, is to agree in a contract for software development that you hand over your modifications to a 3rd party (your client) under the condition that you do not hand it over to other parties. That has nothing to do with the license itself though - it's simple contract law for your work-for-hire. Yet you have to hand over the source code of the LGPL-covered code (at least on request) to your client (and all other parties whom you distribute the binaries to).
As to your client: It certainly depends on jurisdiction, but usually a company is legally a single body, so the license terms for conveying a piece of software do not apply. Yet one might enter a grey area already with companies and subsidiaries.
They certainly may not convey the rebranded (modified or unmodified) software to other 3rd parties under a different license than LGPL. The difference of the LGPL to the GPL is here - in short terms - that the LGPL - licensed software can be used as a module or library to a proprietary-licensed software. Yet any changes to the LGPL-licensed part must remain under LGPL and thus the LGPL terms apply, and sources must be made available, if distributed.
On the other hand, given your question that they ask you to make adoptions to an ERP system: sure, any branding, user-specific UI etc, they are of little interest to anyone; just changing config files to suit your setup and swapping art assets for rebranding is not making changes to the code.
Yet if you develop general improvements to open-source software, you might want to talk to them, consider to push upstream what you can for good reason: Contributing the non-company and non-setup-specific improvements and fixes to upstream to give back to the project you and they use will reduce cost of ownership in the mid- and long term: Thus it will be their profit as it will reduce maintenance and update costs and possible later contractor costs to make changes to their existing themes and needs.