Yes, that's possible. NTAG203 (datasheet) is an ISO/IEC 14443 Type A ("NFC-A") tag and follows the NFC Forum Type 2 Tag Operation specification. In order to activate the physical write protection feature of such a tag, you need to set the lock bits.
On Android, you can access such a tag by obtaining an instance of the NfcA technology connector class for your tag handle:
Tag tag = ... // I assume you already received the tag handle by means of an NFC discovery intent
NfcA nfcA = NfcA.get(tag);
if (nfcA != null) {
// this is an NFC-A tag
...
The lock bits of NTAG203 are located in page 2 (0x02) bytes 2-3 and in page 40 (0x28) bytes 0-1. Each of the bits of those 4 bytes controls the lock state of certain pages of the NTAG203 memory area. In order to activate locking, you have to set the lock bit to '1' by issuing a write command for the pages containing the lock bits. So for the simplest scenario of locking the whole tag, you could do something like this:
// connect to the tag
nfcA.connect();
byte[] result;
// write all-ones to the lock bits on page 0x02
result = nfcA.transceive(new byte[]{
(byte)0xA2, // Command: WRITE
(byte)0x02, // Address: page 0x02 (2)
(byte)0x00, (byte)0x00, (byte)0xFF, (byte)0xFF // Data: set bytes 2-3 to all '1'
});
// write all-ones to the lock bits on page 0x28
result = nfcA.transceive(new byte[]{
(byte)0xA2, // Command: WRITE
(byte)0x02, // Address: page 0x28 (40)
(byte)0xFF, (byte)0x11, (byte)0x00, (byte)0x00 // Data: set byte 0 and lock bits in byte 1 to all '1'
});
nfcA.close();