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<eLinkResult>
	<LinkSet>
		<LinkSetDb>
			<DbTo>nuccore</DbTo>
			<LinkName>gene_nuccore_refseqgene</LinkName>
			<Link>
				<Id>262359905</Id>
			</Link>
		</LinkSetDb>
		<LinkSetDb>
			<DbTo>nuccore</DbTo>
			<LinkName>gene_nuccore_refseqrna</LinkName>
			<Link>
				<Id>237757283</Id>
			</Link>
			<Link>
				<Id>237681126</Id>
			</Link>
			<Link>
				<Id>237681124</Id>
			</Link>
			<Link>
				<Id>237681122</Id>
			</Link>
			<Link>
				<Id>237681120</Id>
			</Link>
			<Link>
				<Id>237681118</Id>
			</Link>
		</LinkSetDb>
	</LinkSet>
</eLinkResult>

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<LinkSetDb>
	<DbTo>nuccore</DbTo>
	<LinkName>gene_nuccore_refseqgene</LinkName>
	<Link>
		<Id>262359905</Id>
	</Link>
</LinkSetDb>

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from lxml import etree


def main():
    root = etree.parse('test.xml')
    ids = root.xpath(
        'LinkSet/LinkSetDb/LinkName[text()=$link_name]/../Link/Id/text()',
        link_name='gene_nuccore_refseqgene'
    )
    print ids  # ['262359905']


if __name__ == '__main__':
    main()

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import xml.etree.ElementTree as ET
xmldata = ET.parse('test.xml')
link_id = next(el.findtext('Link/Id')
    for el in xmldata.findall('LinkSet/LinkSetDb')
        if el.findtext('LinkName') == 'gene_nuccore_refseqgene')