What could be the reason while Troubleshooting LAN Connectivity where Serial is UP, Line protocol is Down ?

For LAN connectivity one should use Ethernet E interface. Instead of Serial S interface.

Anyhow there are many reasons among them are:

1-Protocol mismatch at both ends

2-Configurations are incomplete/incorrect

The reasons can be 

Other side of the interface is shutdown

Encapsulation mismatch

Bandwidth or MTU mismatch

Clock rate not set in DCE end

shut or no shut both interfaces and other problem is  Encapsulation  mismatch!!

Encapsulation mismatch, interface is up as mentioned in the question.

the serial is up line protocol is down ...check  the neighbor interface shutdown (interface is not up )   and other problem is encapsulation  mismatch .

Check Clock Rate, and Bandwidth settings

The encapsulation that is configured on  Router A does not match the

encapsulation that is configured on Router B

My understanding is the first state is physical OSI Layer1. If its down then look for an issue such as cabling.

The line protocol state is L2 issues, most commonly encapsulation mismatch (HDLC vs PPP)

So for Serial0/1 (on both router interfaces)  displaying Serial0/1 is up, line protocol down...

1. I verify the encapsulation type is set for the same type.

2. I verify both interfaces have a unique IP address in the same subnet.

3. Check that bandwidth setting is the same. And MTU value is the same.

4. Understand this is not being caused by a admin shutdown condition (otherwise L1 state would not be up)

5. Assume this would not be a cable problem (wrong cable type, cable not plugged in, cable not seated fully).

CLOCK RATE. This needs to be set on the DCE side of a back to back configuration and it is a favorite of Cisco when it comes to troubleshooting serial interfaces.

The reason is basically;

1. Other end interface might be down.

2. Encapsulation mismatch.

3. MTU miss match.

4. Protocol mismatch.

Line protocol is Down: indicates L2 (ethernet, frame relay, ATM etc) problem

Both serial interface Baud rate must match then only it will communicate each other