Charities have until the end of August to apply for the remaining £1.9m in the programme, which awards up to £15,000 over one or two years to improve systems or pilot new projects.
Organisations in England and Wales with annual incomes of between £25,000 and £1m that help people overcome complex social issues, such as homelessness, addiction and domestic abuse, are eligible to apply.
The grants have been used to help with issues such as business planning, trustee recruitment and marketing projects.
The foundation is closing Enable and its other grants programme Invest as part of its new strategy for 2018 to 2022, Reaching Further, which will focus on providing bigger, long-term grants to fewer organisations.
Applications to Invest, which awards £30,000 to £100,000 over three years for day-to-day running costs and/or direct delivery of its work, have already closed.
The new strategy says the foundation will issue grants of up to £200,000 for up to six years.
Charities awarded Enable grants can sign up for Lloyds Banking Group charity mentors and receive in-kind support from partner consultants and the foundation to overcome specific organisational challenges.
Paul Streets, chief executive of the foundation, said: "We know small and local charities are under real pressure, fighting to keep core services going, and are often less able to focus on their own development.
"By allocating funding specifically for this purpose, we are committed to making charities stronger and more sustainable for the long-term, affording them the headspace to evolve, try new things and cultivate effective and inspirational leaders across the sector."
Details of the foundation's new grants programmes are expected by autumn.
A spokeswoman said: "Grant-making around capacity-building will still be a priority but we’re currently redefining how it looks."
The foundation, which is funded by Lloyds Banking Group, awarded £14.4m to charities in 2018.
For more information about Enable, click here.