I have not found Richard Lamb in newspaper but I found this article which I copied & pasted , gives you an idea of the amount he might have won.
Quite a lot of money in 1802 !!
STATE LOTTERY OFFICE. and Co. 26, Corhbill, Loudon—-Also R. Beatnijff's, Book/eller, tforwicb.~-Ihe Nobility ■ and Gentry are refpeclrully acquainted that the Lottery begins Drawing next Month, and that will be*adviieable to no time in purchaiing Tickets and-Shares, as they will advance. The Scheme, which may be had and t or's approved of.—Clubs and •societies lay their money oitt. they collect it, J not waiting as former Lotteries until two or tliree days before the Drawing.— the.hrft-drawn Ticket has. wonderful attraction £.10,000,. the fecond day, 0,000 the third day, and £.25,000 the fourth day, befides Capital Prizes for every day's drawing. The lait Lottery was quickly dilpoled of—Tickets rofe extravagant price.—The Lottery bids fair to furpals every preceding Lottery. Frizes paid Demand.
After further looking I dont think they gave the names of winners .It was a bit like a raffle where you have a number and the results just say the number drawn