JCT - Assumption in design

We have entered into a JCT lump sum contract.
There are elements we have an adequate amount of monies to build in place.
Even though there was no design or design intent so we made an assumption.
An element has now been designed and is bespoke plus way beyond anything we have allowed for or envisaged.

My question is does the design need to fall within the our budget, or is ,the extra over needs to be paid by client, or are we required to build as they wish as it’s are risk the monies we have allowed fall short even though there was no design at tender?

It’s difficult to answer this one with more specific information however from a general point of view you should have priced to fulfil the Employer’s Requirements that were issued to you at tender stage. If the Employer changes these requirements e.g. issues new / amended design information then you are entitled to be paid for any additional work as a variation and may be entitled to an extension of time and any associated loss and expense.