The controversial Named Person scheme is set to become law in August.
A state representative will be appointed to every child under 18, with health visitors taking on the role for children under five.
Ministers have promised to fund an extra 500 posts across Scotland, with 61 in Lothian, but the health board still faces a rush to fill them in time.
NHS Lothian covers a population of 826,00 people as well as providing care nationally. It currently has 24,000 full and part time staff.
Royal College of Nursing Scotland Associate Director Norman Provan said: “We have significant concerns.
“ Health visitors – who will be the Named Person for children aged 0-5 years – are already under serious pressure, with NHS Lothian experiencing great difficulties recruiting enough now, let alone the additional health visitors they will need to implement the Named Person role and the recently-introduced new health visitor pathway.
“While we welcome the fact that the Scottish Government is providing funding for 500 more health visitors, these additional posts are being phased in and won’t all be in place when the Named Person comes into force in August 2016.
He added: “NHS Lothian needs to redouble its efforts to fill its current health visitor vacancies and look at all the options – including asking the Scottish Government to incentivise recruitment through applying a recruitment premia – to recruit the additional health visitors needed to implement the Named Person legislation.
“What the board cannot, and must not, do is ask the current health visitor workforce to take on more to meet the requirements of the Named Person legislation without sufficient resources to do this safely.”
A Scottish Government spokesman said £41.6m would be invested to provide 500 extra health visitors in Scotland and make sure staffing levels were adequate.
He added: “Health visitors are valued members of the nursing workforce and we remain committed to their vital contribution to improving the health and wellbeing of children, young people and families.
“The role of the Named Person is to provide a single point of contact for parents and children who can help and support them in liaising with other services.”
NHS Lothian said it had put in place a UK-wide recruitment campaign, a speedier recruitment process, an up-skilling programme, intensive training, disruption allowance for Midlothian posts and was working to support recently retired staff return to practice.
Professor Alex McMahon, Interim Nurse Director, NHS Lothian, said:
“Securing our health visitor service is a priority for NHS Lothian and we are encouraged to see that the overall position has not changed significantly which suggests the measures we have put in place are having an impact.
“The slight improvement in Midlothian is encouraging but accept the situation remains challenging.
“To support the named person criteria, 18 newly qualified health visitors are due to take up post in September.”