H1B as a backup option

[CDP1510]

Note: This might be a little complicated situation, so apologies for the long post. 

I was in the US on an H1B with my previous company from 01NOV2003. I then moved to my current organization in Jan 2006, and they filed for my H1B transfer - effective 17JAN2006 valid till 15JAN2009. However, this was always going to be a short term gig, as I was hired for a position in India, and I was in the US primarily for knowledge transfer. I moved back to India on 26MAY2006, and never used up my allotted days on the H1B. Thus, I was in the US only for about 2 years 8 months of the available 6 years on my H1B petitions.  

Since Aug. 2018, I am back in the US as an India employee on assignment in the US, currently on an L1-A visa (expiring Aug. 2021). My company has approached me about converting to US salary role, and is willing to process my permanent residence application. Since my L1 can only be renewed for another 4 years (acc. to what the lawyers told me, the max limit for L1 is 7 years), and at this point the lawyers cannot "guarantee" the green card within 4 years (even though with an L1A, the probability is high), they have recommend to put my name in for the H1B lottery, so that we have some backup options if things take more than the 4 years. This seems logical, so I don't have too many problems with this approach. But I am wondering if I really need to go through the lottery process since I have 3+ years unclaimed on old H1B petitions. 

Am I eligible to recapture the 3+ years on my old petitions or do I have to go through the whole lottery process again as it is almost 15 years since the petitions were valid?