I consulted a number of reference works, handbooks and biographies on Shakespeare to check whether Lope de Vega is mentioned at all. The results are listed below.
A Shakespeare Companion 1564-1964, edited by F. E. Halliday (Penguin 1964) has an entry on Lope de Vega containing the following information:
About the time that Shakespeare was writing Romeo and Juliet, Lope de Vega was also dramatizing the story in his Castelvines y Monteses (Capulets and Montagues). The apparently dead and concealed Julia speaks to her father who thinks it is her ghost and promises to forgive her husband whom she had secretly married. Roselo and Julia appear, and their marriage is ratified.
Both authors were apparently inspired by the same source but this does not imply influence on each other.
The Cambridge Companion to Shakespeare Studies, edited by Stanley Wells (Cambridge University Press, 1986) does not mention Lope de Vega or Spanish literature.
The New Cambridge Companion to Shakespeare, edited by Margareta de Grazia and Stanley Wells (Cambridge University Press, second edition, 2010) does not mention Lope de Vega or Spanish literature, either.
The Bedford Companion to Shakespeare: An Introduction with Documents, edited by Russ McDonald (second edition, Bedford/St. Martin's, 2001) mentions Lope de Vega in a context that has nothing to do with influence:
(...), the Spanish playwright Lope de Vega, a contemporary of Shakespeare, speaks of professional dramatic pirates who went to the theater deliberately to memorize and reproduce plays for print (...).
The German Shakespeare-Handbuch edited by Ina Schabert et al (Stuttgart: Kröner, 1992; almost 1,000 pages) dedicates almost 100 pages to Shakespeare's influence on other authors but does not mention Lope de Vega at all.
Elizabethan-Jacobean Drama: A New Mermaid Background Book, edited by G. Blakemore Evans (London: A & C Black, 1988) mentions neither Lope de Vega nor Spain.
The Renaissance: A Guide to English Renaissance Literature: 1500-1660, edited by Marion Wynne-Davis (Bloomsbury, 1992) contains an entry entitled "Spanish influence on English literature". This entry mentions the English translation of Don Quijote (Part 1 in 1612, i.e. near the end of Shakespeare's theatrical career; Part 2 in 1620, i.e. after Shakespeare's death). The second paragraph in this entry is more relevant (with additional links):
The 16th and 17th centuries in Spain were known as the Golden Age, which paralleled in quality, but greatly exceeded in abundance of texts, the creativity of the Elizabethan and Jacobean ages in England. The plays of Pedro Calderón de la Barca (1600–81) have often been compared to those of Shakespeare. Spanish Golden Age influence on contemporary English drama can be seen in James Shirley's The Young Admiral (1633) and The Opportunity (1634), as well as in Beaumont and Fletcher's Love's Cure (1629).
The examples mentioned here are later than Shakespeare. The third paragraph in this entry discusses translations of prose works but no concrete examples of influence on English literature, let alone Shakespeare's plays.
The Renaissance also contains on entry on "Spanish intrigue comedy" (emphasis added):
English comedy influenced by, or using as its source, a type of Spanish play known as 'comedia de capa y espada' (comedy of cape and sword). The originals include works by Pedro Calderón de la Barca (1600–81), Lope de Vega (1562-1635), and Tirso de Molina (1571–1648). The plays frequently turn on conflicts of love and honour and are dominated by busy intrigue plots involving problems of mistaken identity, duelling and concealment. One of the first of this variety was Sir Samuel Tuke's The Adventure of Five Hours (1663), based on a play by Calderón, and commissioned by Charles II. (...)
In other words, one of the first examples of "Spanish intrigue comedy" was written several decades after Shakespeare's death.
Shakespeare: A Life in Drama by Stanley Wells (Norton, 1995) does not mention Lope de Vega; Spain is only mentioned once (because of the Armada).
Will in the World: How Shakespeare Became Shakespeare by Stephen Greenblatt (Jonathan Cape, 2004) does not mention Lope de Vega. Greenblatt discusses Spain mainly in the context of political relations between that country and England or when mentioning Queen Elizabeth's physician Roderigo Lopez, who was executed in 1594 on an accusation of an attempt to poison the queen.
Shakespeare: The Biography by Peter Ackroyd (Chatto & Windus, 2005) does not mention Lope de Vega; Spain is mentioned only in the context of political relationships.
Germaine Greer's book Shakespeare's Wife does not mention Lope de Vega or Spanish literature. The only entry for "Spain" in the index refers to a passage in Chapter 10 that mentions that England imported steel knitting needles from Spain before the 1570s. (Knitting needles made in England were made out of wood or bone.)
After consulting eleven sources on Shakespeare and English Renaissance literature, I am not aware of any concrete examples of influence by Lope de Vega on Shakespeare. Influence in the opposite direction, if any existed, would be easier to find in works on Lope de Vega.
