Yea... This is a little tricky to explain in this forum if I read the question right, and its a bit technical.
eg I have to explain what a scale factor is, and its dependancies on various things we observe. But let me proceed anyway.
In general you will have a ratio of energy densities like so:
Lambda (Vacuum) / Lambda (Matter) ~ a^3. Where a is the scale factor whose second derivative measures the 'acceleration' of the universe (I hate to use the word acceleration here btw, it can easily lead people astray if they're not careful, and there are several different inequivalent parameters that you might be thinking off). That means in early times matter and radiation are dominant, and vacuum energy irrelevant, whereas at late times the reverse happens.
And yes, acceleration was slower in the past. you'd need to look at the acceleration equation for a FRW universe for the full picture... roughly it looks something like this off the top of my head
acceleration/a ~ -(p(m) + p(vacuum)) > 0 where acceleration is the second derivative of a, and p(m) and p(vacuum) are linear functions of rho matter and rho vacuum (the energy densities).. Theres a bunch of constants and stuff floating around that im neglecting, and im taking some confusing liberties with definitions here, but thats roughly the idea.
You might want to check one of the exhaustive cosmology faqs out there on FRW universes with the concordance model parameters.