Have lottery winnings of $1,000. Can I claim lottery losses more than that amount for which I have receipts?

Yes, but in the unlikely case of an audit, it might not hold up. Typically if you can show a pattern, such as weekly purchases, you might survive an audit.

But, as eastsidr indicated, you question is somewhat academic. Gambling losses are only deductible as an itemized deduction. So, if you use the standard deduction, like 74% of taxpayers, all your $1000 winning will be subject to taxation

No.  Unfortunately, gambling losses are deductible only to the extent of winnings.  If you have other gambling wins/income and report those winnings, you can then deduct losses to the extent of the total lottery and other wins.  The losses are deductible on Schedule A (Miscellaneous Deductions) if you itemize deductions.  The winnings are reported on Form 1040, Other Income.