What I also found out already is that the SPI connections do interfere with the I2C - not sure why, but the scanner works best when the SPI is disconnected (using a Pro Micro as SPI programmer - it's as if the pins are not set to INPUT when the programmer is finished).
The ATtiny family does have hardware support for SPI and I2C but that support is not directly comparable with the support the ATmega family offers. In the Tiny world USI (Universal Serial Interface) is responsible to provide that hardware support for both interface types. That also means you cannot use both on the same chip.
I'm using ATtinycore, and trying to use the built-in Wire library and the LiquidCrystal_I2C library. This doesn't even compile: turns out the problem is that the 841 doesn't have I2C master hardware, so that's done in software, and that's clashing with the LiquidCrystal_I2C library.
On my machine the HelloWorld example of LiquidCrystal_I2C compiles without an error for the ATtiny841(optiboot). Please post the code that fails for you.