Well, if the random LFO in Renoise is even remotely similar to other number generators I’ve experienced, then it’s not truly random in the first place… it’s a psuedo-random number generator which already has to be initialised with some kind of seed value. Typically, this seed might be based on the current system time/date, or some other suitable piece of ‘unique’ data.
For example, a seed value of “1” might produce the sequence “1, 4, 6, 2, 8, 3…”
While a seed value of “2” might produce the sequence “5, 3, 8, 1, 0, 4…”
etc.
These sequences are still ‘random’, because you can leave the generator running for a long time and get completely different results, but they are also predictable, because you can guarantee that a particular seed will produce exactly the same sequence of numbers every time.
I am not suggesting that the core behaviour needs to be changed in any serious way. For other users who decide to never touch the reset function (which is currently rather useless in random mode anyway), then the LFO will behave in exactly the same way as it always has, and Renoise will seed the number generator using whatever method it currently uses. But it should also be possible to override that default behaviour by supplying a custom seed value, if I choose to.
That simple element of control is really the key issue here for me: Every time I render my song, I need to be able to rely on the output being identical every time, even if I am using a random LFO.
Even though I use randomised behaviours to help me add some varied/organic feeling to things, I need to remain in control of the overall process so that I can actually create music with a specific intention, rather than being at the mercy of completely unpredictable system.
I’m a control freak 
.