As far as I know, there are two feasible cases:

1. The customer MOVES from one ISP to another 2. The customer connects to ANOTHER ISP, while using the other ISP

Hi, Many Thanks for all comments. The case I meant was exactly the 2nd one. Customer has an old connectivity to LIR-1 and have got a new connection from LIR-2.

2 is usually performed either by the use of BGP or by the use of static asymmetric routing, or RADWare's LinkProof.

That's the case.

In the 2nd case, the reason here is usually high availability and/or load balancing between links/ISPs. In this situation, the customer NEEDS both the assignments.

In this case, what should people at LIR-1 Do? Can they ask LIR-2 people to stop forcing customers? And if the answer is positive, What's the rule, if LIR-2 people continue to behave like that?

I believe that 'legal', a LIR cannot just 'demand' that a customer would return their previously-assigned IPs unless there's a reason (i.e., the situation is case #1). It might be that that specific LIR is having problems with its AW (let's say their AW is 256 ips, and the customer already has IPs, it might be that the 'new' LIR needs to send a RIPE-141 to RIPE - and they might be too lazy to do that).

I agree. Another possiblity is that LIR-2's people are trying to fulfill their own test period ( according to RIPE NCC slow starting ) and somehow attack to LIR-1 reputation. Kind Regards, IPM LOCAL REGISTRY, Tehran-Iran Saeed.