No, they can't mix....
The LIRA is used to buy a LIF or a LRIF. (Life income fund, the purpose is to provide $'s for life) This is to guarantee that there is still money left when you are 80 and has maximums you can withdraw, as well as minimums. These two differ in that the LIF amount must be converted to an annuity at age 80, and an LRIF does not and can be passed on to heirs if you die after age 80.
The RRSP goes into the RRIF, which has minimums you need to withdraw starting at age 72 (needs to be converted the year you turn 71 but can be converted earlier.)
What you CAN do is buy a registered annuity using either RRSP and LRIF funds.. instead of a LIF. I can't see why there would be restrictions in the source of the funds used to buy annuities, but even if there technically are, the payouts would come monthly and look like a single source in practical life.
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The exception to this "No Mixing" is that there is the ability to unlock all or a portion of your LIRA and convert it to an RRSP / other fund.
I was able to unlock a portion when I terminated (only the value of the portion I contributed, I think, the company portion was locked), and if the total fund is very small you can unlock it all... if you are terminated after 55 (check the age / rules, but I think this is where you see the age 55 in your thinking - it is related to unlocking rules) you can unlock additional amounts within a short time after termination. ** I am fuzzy on the details -- need to look them up!!***
But the portions that stay locked, can't be merged because of the different rules about how to access them after age 71.
ETA -- Unlocking provisions vary by province (which is why I was fuzzy on them)
Financial hardship is one reason (about to lose home, foreclosure, medical bills in ON, AB, NS)
50% unlocking after age 55 (can do this one time)
You are no longer a Canadian resident (allowed by 7 provinces).
Small balance (e.g., under $11k for several provinces, varies, ON & MB is $21k)
Smallish balance and age 65 or older ($21k for QC, BC, AB, NS)
Shortened life expectancy -- terrible reason... you are expected to die so you can access your money.
Very Low income (ON, AB, NS), e.g., income under $37k and you can unlock up to $27k per year (sliding scale).