* Dollar Libor eases, spread vs OIS steady

* Euro, sterling Libor/OIS spreads narrowest in 3 months

(Updates with Libor fixing, adds byline, pvs SINGAPORE)

By Ian Chua

LONDON, Jan 6 (Reuters) - The cost of borrowing three month dollar, euro and sterling funds between banks eased on Tuesday, keeping intact expectations the interbank money market will continue to heal in the new year after a stressful 2008.

The collapse of top names such as Lehman Brothers last year dealt a severe blow to confidence among banks, causing lending between financial institutions to grind to a halt.

Central banks around the world have since been providing banks with cash and have introduced other measures such as guaranteeing their debt, helping calm the interbank money market.

The big question this year is whether banks will start lending to each other again without central bank assistance, analysts say.

The behaviour of London interbank offered rates (Libor) over the coming days and weeks will be a crucial signal of whether or not liquidity is returning to money markets, said London-based Laurence Mutkin, analyst at Morgan Stanley.