The assessments have been brought in following the death of a staff member, Don Grant, while on the job in April 2022.
Grant died when he was struck and killed by coal being moved from the port via a conveyor belt and loaded onto a cargo ship by a jet-slinger.
Last month, LPC was fined about $500,000.
Maritime Union of New Zealand (MUNZ) said LPC pleaded guilty in November 2023 to one charge under the Health and Safety at Work Act 2015 brought by industry regulator Maritime NZ.
Union national secretary Carl Findlay said workers welcomed the guilty plea and sentencing, and a lot had changed since Grant's death - including around work practices involving coal operations.
But workers were concerned about a mandatory fitness for work programme for employees, he said.
"The workforce is just shocked and disappointed that the port company seems to be using Don's death as a catalyst to driving in a mandatory medical assessment, and the union is not having any input or say into what that looks like. In our view, it basically takes away any right of the employee's privacy."
Findlay said this had been pushed through without regard to workers' concerns over their financial protection and the wellbeing of any members who failed the assessment, with the ultimate result of people losing employment if they did not meet the standard.
"In short, MUNZ see this as a breach of good faith and LPC not honouring our Collective Employment Agreement."
The union was agreeable to fitness for work health monitoring, but wanted LPC to negotiate in good faith, Findlay said.
"We want to have a talk about this mandatory testing and how that's all going to look and roll out. There's not just one job down on the waterfront, there's several jobs, so what will that look like if you weren't fit to do a certain duty, could you possibly do another duty? We're guessing they're thinking 'if you're not fit for that job you're not fit for any job so you're out'," he said.
Lyttelton Port Company chief executive Graeme Sumner said accident investigators recommended mandatory health assessments after Grant's death.
LPC said these were introduced on 31 July, and had been standard for new employees since 2023.
"LPC's introduction of mandatory health assessments follows the TAIC report's recommendation after the tragic accident on ANZAC Day 2022," Sumner said.
"The health assessments are crucial for identifying employees who may need support with a comprehensive health management plan and rehabilitation. This initiative aligns with our obligations under the Health & Safety at Work Act 2015 to prevent harm to our workers and others due to health-related limitations in performing their duties safely."
Sumner said the company had undertaken full consultation with staff and unions.
"Since June 2022, we have engaged in meaningful dialogue with our staff and unions regarding health monitoring. It was outlined in our annual report last year, and our feedback to TAIC was included in their report. It has also been standard for new employees since 2023.
"We've addressed all queries throughout the consultation and feedback process, which formally began on 1 May 2024. RMTU [Rail and Maritime Transport Union] requested an extension of the feedback period, which was granted, reflecting our commitment to thorough and inclusive communication.
"The decision document was shared with all staff following the consultation's conclusion on 20 June 2024. All unions were informed of the decision 24 hours prior to the broader organisational communication. LPC will continue to engage with our unions using in good faith consultation and in a collaborative and cooperative manner, as we have been doing."
Rail and Maritime Transport Union disputed this, saying there was no meaningful engagement in the decision-making process.
"LPC saying they considered RMTU's feedback within their consultation process of the MHA [Mandatory Health Assessment] is a clear example of this. LPC did not make any changes to the MHA at any stage of the process, basically, they came up with a plan, then went away and tried to work out how they would force it on the workforce, and that is what they have done," the union said.
The Maritime Union said it was attending mediation with LPC on 16 August on the issue of health monitoring.