I know quite a bit about how this operates as I work in a relevant field.
The Defence argue a case based on their client's instructions. So the client will give their account of what happened, eg. 'It wasn't me, it was my brother Fred Bloggs, it can't have been me because I was down the pub at the time.' The Defence team will then call whatever witnesses they can find who will support that view. That might be an expert witness saying, 'I examined the pint glass and found the DNA of Joe Bloggs, which is consistent with him having been in the pub', or it might be the pub landlord saying, 'Yes, Joe was definitely there that night because he argued with me about the Arsenal match.'
If the witnesses don't support the account Joe Bloggs has given to his Defence team, then the barristers will point this out to Joe, and suggest that his account is unlikely to be believed by the jury. But ultimately if he sticks to his story, no matter how implausible, that is the argument the Defence will present in Court. What the Defence can't do, contrary to popular belief, is say to their client, 'Look, this story is ridiculous, you'd be much better off arguing XYZ instead'. They also cannot argue a defence if the client has admitted to them that he is guilty but wants them to argue his innocence anyway. That does occasionally happen, and in that case the Defence will have to withdraw from the case (it's rather splendidly called being 'professionally embarrassed').
The cost of expert witnesses will not have been an issue. The rates expert witnesses can charge in criminal cases are laid down by the Legal Aid Agency - the fee rates are commensurate with reasonable reimbursement for the professional time of experienced specialists, so it will add up if they have hours and hours of work do to looking at lab samples or whatever. But the cost would really not have been a barrier - this is major murder trial, if they had found an expert or a professional witness whose evidence they thought would support LL's case, then the costs would have been authorised, and he or she would have been called. Much more likely is that they did in fact instruct multiple expert witnesses to re-examine everything from medical notes to scans to blood reports to HR records, but that the resulting reports were not considered helpful to the Defence case, and hence the expert witnesses would not have been called to give evidence before the Court.