I needed multiple free pins with ATtiny85 so used the NRFLite 2 pins solution for Rx. The Tx needed to be run in conjunction with a RPI which is supported with nRF24 library (https://github.com/nRF24/RF24). To used the default of NRFLite, the RF24 has to configured with set of settings. This combines advantages of both worlds. It might be usefull for other users as well so might be added to the readme. Required settings:

const uint64_t pipes[2] = { 0x0004030201LL, 0x0104030201LL };
radio.setChannel(100); // channel 100
radio.setPALevel(RF24_PA_MAX); // MAX power
radio.setDataRate(RF24_2MBPS); // 2MBPS
radio.setRetries(1, 15); // 250+1*250us delay, 15 retries
radio.enableDynamicAck(); // Enable auto ack
radio.enableAckPayload(); // enable payload with ack and dynamic payload length
radio.setCRCLength(RF24_CRC_8); // CRC8
radio.openWritingPipe(pipes[0]);
radio.openReadingPipe(1, pipes[1]);
radio.write(&_radioData, sizeof(_radioData), true)

Attached sketch of Basic_TX based on RF24 library which works with Basic_RX.
Same Basic_TX but now as python script run on RPI

Basic_TX_RF24.ino.txt
Basic_TX.py.txt