ndeed it looks very much like two software I2C implementations clash - but I wonder where the second could possibly be? I do expect that an LCD library does not try to implement a software I2C, but instead will just try to use the standard Wire library, and let Wire figure out how the I2C works under the hood.
You NewLiquidCrystal library include SoftI2CMaster which is a software I2C emulation. And the ATtiny core also has a software I2C emulation.
Remove the LCD.h from your sketch and use the included version of LiquidCrystal_I2C, that one works with the Wire library provided by the ATtinycore.